Technical Notes

Status: Draft, 2026-09-03 (all cited sources accessed 2026-09-03).

Scope note. These notes turn the standardized composite 4세대 실손의료보험 (silson uiryo boheom, fourth-generation indemnity medical insurance) of product-spec.md (same directory) into a reference liability cash-flow projection on paper, and then into Medical_KR_S beside it. They describe no single insurer’s contract — and on this product they could not, because the benefit definition is not written by a carrier at all: it is the 표준약관 (pyojun yakgwan, standard policy conditions) annexed to the 보험업감독업무시행세칙 at 별표 15 under 제5-13조제1항 [S1] REG-R23 REG-R25. [S#] and [R#] tags resolve against sources.md, whose numbering is carried verbatim from _research/indemnity-medical.md and is frozen; [REG-R#] tags resolve against the cross-product reference library references/regulatory-and-actuarial-references.md, whose own R-numbering is separate and also frozen. std marks a standardization introduced for the reference implementation, always with a rationale and, where one exists, the observed range; unverified marks a claim that could not be confirmed against a retrieved document.

Every contractual parameter these notes share with product-spec.md carries the same value there. What these notes add is the whole modelling basis, which the specification does not carry because none of it is contractual and none of it is public: the claim frequencies by sex and age band, the eight severity distributions the deductibles bite into, the ten-bucket annual-claim shape the experience-rating loop runs on, the mortality and lapse decrements, and the expense and commission split. Every one of them is introduced below as std, and the reason is a positive finding rather than a failed retrieval: 보험개발원 is the statutory 보험요율 산출기관 under 보험업법 제176조 REG-R4, and 실손의료보험 is not among the 장기손해보험 categories whose 참조순보험요율 it publishes R20; the 산출방법서, where an insurer’s 예정위험률 and 예정사업비율 live, is a 기초서류 that is filed and never disclosed REG-R2. There is no public Korean indemnity-medical morbidity or severity basis at all.

This product stands alone in krlib. It inherits nothing from whole life (종신보험), term life (정기보험) or cancer (암보험), and no other product states a delta against it. The reason is structural. 보험업감독규정 제7-63조제1항제2호 lets a 제3보험 benefit be designed on a 정액 (jeongaek, fixed-sum) basis or on the basis of 「실제 발생하는 손해(이하 “실손해”라 한다)」 REG-R17 R19, and this is the only contract in the repository that takes the second branch. There is no 보험가입금액 that determines a claim here, only an annual limit that caps one. So the model is

claim = frequency x severity x (co-payment, deductible, per-visit cap,
                                per-act money and count caps, annual aggregate)

and then — uniquely — the claim feeds back into next year’s premium through the 비급여 할인·할증 (bigeubyeo harin-halchung, non-covered experience discount and surcharge). That loop is modelled, not described.

Three structural facts orient everything below and are worth stating before any arithmetic:

• The contract is one year long. It renews annually at the attained age and the then-current basis inside a supervisory corridor of ±25% per 위험구분단위, and it re-enters the then-current generation every five years [S1 제30조] [S1 제23조] REG-R17 제7-63조제2항제3호·제6호나목. The projection horizon is a stated one, not a contractual one.

• The insured loss is exogenous. Both halves of it — the statutory co-payment on treatment inside the public list and the whole of the treatment outside it — are set by the health ministry and by providers, not by the insurer R7 REG-R53. The boundary between 급여 (geubyeo, treatment covered by 국민건강보험) and the 비급여 outside it moves within any realistic projection horizon.

• Half the claim is truncated by a public scheme. The 본인부담상한제 refunds a member’s annual statutory co-payment above an income-graded ceiling, and the 표준약관 excludes the refundable amount from cover outright [S1 제4조제3항제1호] [S1 제5조제3항] R10 REG-R53. The 급여 half of the claim is therefore bounded above, and bounded differently by income decile. The 비급여 half is not bounded at all.

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Model scope and conventions

• Purpose. Project gross best-estimate liability cash flows per policy issued — office premiums on the two separately re-rated priced units, the five benefit limbs, maintenance expense, claim-handling expense and commission — for a single model point, undiscounted and gross of reinsurance. Korea runs three measurement bases over one such stream and all three are live: K-IFRS 제1117호 mandatory since 2023-01-01 REG-R60, K-ICS in the same quarter REG-R13, and the 해약환급금준비금 that has no counterpart anywhere else in this repository REG-R11. This model stops deliberately before all three and keeps the cash flows basis-agnostic. Discounting, the risk adjustment, the CSM, 요구자본 and every reserve are out of scope and are cited, not reproduced — see Valuation and reserve pointers.

• Projection frequency. Monthly grid, because the product is: 월납 is the only premium mode retrieved and the whole published FSS premium series is monthly [S3] [S4] R7 R8. t is the policy month and is 0-based: the first projected month is t = 0, the frame is t = 0, 1, …, proj_len() − 1, and month t is the interval from t to t + 1 months after the 계약일. proj_len() is the number of projected months — the exclusive end of the frame, not the last index — so result_cf() has proj_len() rows, 120 on the anchor cell. The policy year is the contractual 1-based label y = policy_year(t) = ⌊t/12⌋ + 1, derived from t and never used to index the frame.

• But every contractual mechanism is annual. The 「연간」 of this contract is 「계약일로부터 매1년 단위로 도래하는 계약해당일 전일까지의 기간」 [S1 제5조제2항] — a policy year from the contract date, not a calendar year. All four ₩50,000,000 limits, the ₩200,000 per-visit cap, the 100-visit count, the three 3대비급여 sub-limits, the ₩2,000,000 inpatient co-payment cap, the relativity lookback and the premium itself run on that clock and reset on it. So every benefit and premium quantity is computed per policy year y and spread evenly across the twelve months of that year — the month is a presentation grid for an annual quantity, not a unit of account. Cells that live on the policy year take y and never t; the library spells the two clocks apart on purpose.

• Timing conventions std. Office premium received at the start of month t; claims, maintenance expense, claim-handling expense and commission at the end of month t; decrements at the end of month t in the order mortality → lapse → suspension → renewal decline, the renewal decline acting only where (t + 1) mod 12 = 0, and the maturity count only at t = proj_len() − 1. pols_if(t) is the start-of-month in-force probability and is the weight on every cash flow on the same result_cf() row. Nothing published fixes the decrement order and at these rates it is worth less than a basis point a year.

• Within-year spread std. The annual claim is divided by twelve. No within-year seasonality for this product was retrieved, and since every contractual mechanism resets annually there is nothing for a seasonal pattern to interact with. The consequence to keep in view: a limit that binds part-way through a policy year in reality binds proportionally across all twelve months here.

• Age basis — and the two conventions must both be stated. The projection is on 만나이 (man nai, age last birthday), age(t) = x + floor(t / 12), incremented at the policy anniversary. The contract is not: it prices and renews on 보험나이 (boheom nai, insurance age), the 만나이 at the 계약일 with a fraction under six months discarded and six months or more rounded up, and the 표준약관 works the arithmetic in its own example — 생년월일 1988-10-02, 계약일 2014-04-13, a difference of 25년 6월 11일 ⇒ 26세 [S1 제21조] REG-R25. The model carries 만나이 std because every calibration statistic available for this product is compiled on it — the NHIS coverage ratios by age band R9 REG-R41, the 생명표 decrement REG-R38, the FSS premium series R7 R8 — and because a deterministic single-cell projection cannot represent the distribution of issue dates within the year that separates the two. The two differ for half of all issue dates, so the difference is a half-year of age on average, and it is recorded here rather than silently absorbed.

• Termination and horizon. proj_len() = 12 × min(reentry_cycles × reentry_period, max_cover_age − x), a month count, so the last projected month is t = proj_len() − 1. With reentry_period = 5, reentry_cycles = 2 and max_cover_age = 100, that is two five-year 보장내용 변경주기 — ten policy years — on every shipped model point; the age ceiling never binds on the shipped issue ages. The horizon is stated, and the distinction is the whole point. 감독규정 제7-63조제2항제6호나목 requires the 보험기간 및 보장내용 변경주기 to be five years or less REG-R17; at the fifth 계약해당일 a 4세대 contract’s benefit terms are replaced by whatever the supervisor is then prescribing, at a premium the insurer sets for that product [S1 제23조]. No projection of this contract past the first 재가입 is a projection of this contract’s terms. The model assumes re-entry on unchanged terms, twice over, and says so.

• Contract boundary. Genuinely contestable, and this document asserts no answer: a one-year term, an unrestricted right to re-rate at renewal, a supervisor-set ±25% cap on that re-rating, a five-year re-entry into a wording the insurer does not control, and an obligation not to refuse re-entry on health grounds [S1 제23조제1항] R2. Nothing retrieved states an industry or supervisory position on where the IFRS 17 boundary falls for that combination unverified. Note the sentence that pulls the other way: 「종전 계약을 자동갱신하거나 같은 회사의 보험상품에 재가입하는 경우에는 종전 계약의 보험기간을 연장하는 것으로 보아」 [S1 제3조제6항] — for benefit purposes renewal and re-entry are continuations, not terminations.

• Currency and rounding. KRW throughout. Intermediates at full double precision. Displayed cash flows to ₩0.0001 and pols_if to ten decimals std — the expected values are fractional, the amounts are small, and the test suite asserts the worked example at the displayed precision. Monthly rows rounded for display do not re-add to the displayed annual totals; the totals are sums of unrounded values.

• Model points. One policy at a time, projected on a probability-weighted basis; pols_if(t) multiplies each per-policy cash flow, so result_cf() is a unit projection and scales linearly. Projection is parameterized by point_id; no aggregation logic is specified here. Ten model points ship; point_id = 1 is the anchor cell of the Worked example below and the test suite’s target.

• Sign convention. net_cf is income-positive — premiums less claims, less maintenance expense, less claim-handling expense, less commission. That is the library-wide sign and these notes’ own, so unlike whole life and immediate annuity there is no outgo-positive liability_cf companion to publish: one stream, one sign, one name.

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Model point attributes

Attribute	Type	Anchor cell (point_id = 1)	Cells
sex	enum {M, F}	M	sex()
issue_age (x)	int, 만나이, 0–65 std	40	issue_age()
premium (P₀)	KRW a month, office premium, first policy year only	11,982	premium_mth_pp()
np_share (s)	비급여 share of the first-year premium	0.60 std	np_share()
np_rider	bool — 실손의료보험 특별약관 (비급여) held	1	np_rider()
three_np	bool — 3대비급여형 held (inside the rider)	1	three_np()
annual_limit (L)	KRW a year per 보장종목	50,000,000	annual_limit()
visit_cap (Lv)	KRW per outpatient visit	200,000	visit_cap()
oop_decile	int 1–10, NHI-contribution decile; the anchor’s rung std, the scale itself R10	6	oop_decile()
clinic_share	share of 급여 통원 at the ₩10,000 tier	0.63 std	clinic_share()
nhi_covered	bool — inside 국민건강보험 / 의료급여	1	nhi_covered()
trend_mult (k_trend)	multiplier on both cost trends std	1.0	trend_mult()
util_mult (k_util)	multiplier on every claim frequency std	1.0	util_mult()
reld_on	bool — 요율 상대도 in operation	1	reld_on()
noclaim_on	bool — 무사고 할인 in operation	1	noclaim_on()
suspend_rate	annual 개인실손 중지 decrement std	0.00	suspend_rate()
label	str	anchor 40M all covers full limit	—

Four of these deserve a note, because each is a model point column somewhere else in the library and a state here.

premium is an input, not a computed quantity, and it has an authoritative anchor. The joint FSC/FSS launch release prints ₩11,982 as the 4세대 premium for a 40세 남자 on a 10-carrier 손해보험 average as at 2021-06, against 1세대 ₩40,749, 2세대 ₩24,738 and 3세대 ₩13,326 for the same insured R1. Age 40 male is also the 기준연령 요건 of 감독규정 제1-2조제2호 — 「전기납 및 월납 조건으로 남자가 만 40세」 — so the anchor cell is the cell Korean supervisory disclosure is quoted on REG-R9. No age × sex rate scale exists in public for any generation: the 손해보험협회 comparison grid is filtered by 성별 and 보험나이 and by nothing else, which is the disclosure’s own confirmation that the scale is an age × sex table, but the grid is POST-driven and returned 「조회된 내용이 없습니다」 to a plain fetcher [S7] REG-R62. The other nine model points’ premiums are therefore std and are round-number levels, set in the neighbourhood of the anchor carried to the issue age at the 4.0% age slope but not computed from it — they sit within about ±5% of 11,982 × 1.04^(x − 40) at ages 35 to 65, further away at age 30, and the age-0 rung is a floor rather than a slope value. Model point 5 is the exception and is arithmetic: at np_share = 0, ₩4,793 is the anchor’s 급여 half to the won. Only the first policy year is an input; every later year is the renewal recursion of prem_ge_base and prem_np_base.

oop_decile is a model point attribute and not an assumption, because the 본인부담상한액 is set by the insured’s own income and the spread is nine-fold: on the 2026 scale a 1분위 insured is refunded everything above ₩900,000 a year and a 10분위 insured everything above ₩8,430,000 R10. The 급여 claim distribution is truncated, and truncated differently by income. That is why the 비급여 half, which has no such truncation, was 57.1% of all claims paid in 2025 against a 15.8% share of national spend R7 R9.

nhi_covered is a state, not an event. Where the insured falls outside 국민건강보험법 제5조·제53조·제54조 or the 의료급여법 equivalents — most commonly a suspension of entitlement — reimbursement falls to 40% of the amount actually borne on both parts, still within the annual limit [S1 제3조제3항제1호] [S1 특별약관 제3조제8항]. It persists while entitlement is suspended, so it belongs on the model point and not in a transition. The wording states the reimbursement; this model states the retention, retain_rate_nonhi = 0.60 std, with the flat outpatient deductible floors unchanged on top. nhi_covered = 0 also switches the 본인부담상한제 off, because a life outside the scheme is not refunded by it.

clinic_share carries the provider mix, which is a first-order variable here and in nothing else in the library. The 표준약관’s 급여 통원 deductible table has exactly two rows — ₩10,000 at 의료법 제3조제2항 institutions other than 종합병원, at 보건소·보건의료원·보건지소, at 보건진료소 and their pharmacies; ₩20,000 at 전문요양기관, 상급종합병원, 종합병원 and their pharmacies [S1 기본형 제3조 <표1>]. 0.63 is the 2025 claim split by provider class — 의원 32.0%, 병원 21.8%, 요양병원 2.8% against 종합병원 17.6% and 상급종합 15.0% R7 — normalised over the named classes std.

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State variables

Variable	Description	Updated	Cells
pols_if(t)	In-force probability at the start of month t; pols_if(0) = 1	monthly	pols_if(t)
age(t)	Attained 만나이, x + floor(t/12)	annually	age(t)
policy_year(t)	floor(t/12) + 1; the clock every contractual limit runs on	annually	policy_year(t)
util_band(y)	Lower edge of the five-year utilisation band at the attained age	annually	util_band(y)
prem_ge_base(y)	급여 주계약 기준보험료 a month — a recursion in y, and therefore state	annually	prem_ge_base(y)
prem_np_base(y)	비급여 특약 기준보험료 a month, likewise	annually	prem_np_base(y)
claims_np_rated_pp(y)	The rated 비급여 claim of year y; it is year y+1’s band input	annually	claims_np_rated_pp(y)
band_share(y, b)	The 요율 상대도 band mix at the renewal opening year y	annually	band_share(y, b)
noclaim_share(y)	Share earning the 무사고 할인 — a two-year reach-back	annually	noclaim_share(y)
mort_rate_mth(t), lapse_rate_mth(t)	Monthly decrement rates applied in month t	lookup	—
net_cf(t)	Net cash flow of month t, insurer perspective, income-positive	monthly	net_cf(t)

All of this product’s memory is in the premium, and none of it is in the benefit. That is the exact inverse of the jplib medical chassis, whose 通算 day ledgers carry benefit consumption across the whole of life while the premium is level and never looks back. Here every benefit limit — the four ₩50,000,000 aggregates, the three 3대비급여 money caps, the two 50-act counters, the 100-visit cap, the ₩2,000,000 inpatient co-payment cap — resets at each 계약해당일 [S1 제5조제2항], so no benefit ledger survives a policy year and there is no cross-year benefit state to carry at all. The premium, by contrast, is a recursion: prem_ge_base and prem_np_base each depend on their own prior value, the band mix depends on the prior year’s claim, and the 무사고 할인 depends on the two prior years. A modeller arriving from jplib will look for a ledger and should not build one; a modeller arriving from a level-premium chassis will look for a fixed premium and must not hard-code one.

The band state is memoryless, and that is sourced. 「보험금 지급(사고) 이력이 1년마다 초기화됩니다 … 21년 지급보험금을 많이 받은 경우 → 22년 보험료 할증, 22년 무사고 → 23년 보험료는 할인등급(1등급)으로 초기화」 R2. A single bad year cannot compound into a permanently higher premium and a single clean year returns the policyholder to the discount band. So the band at renewal y is a function of the claim experience of year y − 1 alone: there is no no-claims ladder and no Markov chain to carry, and band_share(y, b) is simply the annual-claim distribution of year y − 1 read against fixed money thresholds. That is what makes the loop tractable in a projection model at all.

Four absences are product facts, not gaps.

• No surrender-value state. 「이 상품은 1년만기 순수보장성 상품으로 해약환급금이 발생하지 않습니다」 [S3], so there is no cv_pp, no claims_lapse, no 보험계약대출 and no 보험료 자동대출납입. A missed premium really does lapse the policy: a 납입최고 of at least 14 days runs and the contract terminates the day after it ends REG-R25 제26조, and 표준약관 제33조 excludes 「순수보장성보험 등」 from policy lending anyway. A policyholder who cancels mid-term recovers the 미경과보험료 under 상법 제649조 REG-R49, which is a return of premium and not a surrender value.

• No death benefit. 감독규정 제7-63조제1항제1호 requires every 제3보험 product to pay the 계약자적립액 and the 미경과보험료 of 제7-66조제5항 on death from a non-covered cause REG-R17 REG-R25 제22조; on a one-year pure protection contract the 계약자적립액 is nil to the precision this model works at, so the payment reduces to the return of unearned premium and there is no claims_death. This is the only place in krlib where that provision has no financial content — in cancer and long-term care the same clause forces an account balance into a non-savings product. Mortality here is a pure liability release.

• No waiting period on the general cover: cover attaches at 보장개시 and the only deferred item is a two-year wait on the 불임관련 질환 급여 cover introduced at 4세대 [S1 제24조] R1. That is unusual among Korean health products and is a direct consequence of the indemnity form — there is no lump sum to anti-select against.

• No premium waiver. No 납입면제 provision appears in either retrieved 실손 wording [S1] [S3]. The absence is unverified as an absence rather than proved, and it is the one place these notes would change materially if a wording turned up that had one.

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Assumption inputs

(a) Contractual / guaranteed elements (cited; the insurer cannot change them)

Every row here is a clause of the 표준약관 or of 감독규정 제7-63조. This product’s benefit half reaches a citation precision no other product in this repository reaches, and the reason is that its benefit definition is a piece of published subordinate legislation rather than a carrier document [S1] REG-R23 REG-R25.

Input	Value	Cells / Reference	Basis
급여 입원 자기부담률	20% of 본인부담금; benefit is 「본인부담금의 80%」	retain_rate_ge_base = 0.20	[S1 기본형 제3조]
급여 입원 annual co-payment cap	Retained inpatient co-payment above ₩2,000,000 a policy year is reimbursed	cap_inpatient_retain = 2000000	[S1 제5조제4항] REG-R17 제7-63조제2항제2호; also in a 2세대 document [S4]
급여 통원 deductible	max(d_tier, 20% × cost), d_tier = ₩10,000 clinic tier / ₩20,000 hospital tier	ded_clinic, ded_hospital	[S1 기본형 제3조 <표1>]
Per-visit outpatient cap	₩200,000, both limbs	visit_cap()	[S1 제5조제5항]
비급여 입원 자기부담률	30% of the non-covered cost excluding the room differential	retain_rate_np_base = 0.30	[S1 특별약관 제3조]
상급병실료 차액	50% of the non-covered room charge, capped at ₩100,000 per day averaged over the whole admission	room_rate = 0.50, room_cap_day = 100000	[S1 특별약관 제3조]
비급여 통원 deductible	max(₩30,000, 30% × cost) — flat at every provider, not tiered	ded_np_out = 30000	[S1 특별약관 <표1>]
비급여 통원 count cap	100 visits a policy year; the only count limit outside 3대비급여	visit_limit_np = 100	[S1 특별약관]
Annual limit	₩50,000,000 a policy year per 보장종목; 상해 and 질병 carry separate limits	annual_limit()	ceiling [S1 제5조]; election std
3대비급여 money limits	도수·체외충격파·증식 ₩3,500,000; 주사료 ₩2,500,000; MRI ₩3,000,000	limit_physio, limit_inject, limit_mri	[S1 특별약관 제3조(3) <표1>]
3대비급여 count limits	50 acts shared by the physical-therapy trio; 50 acts for injections; none for MRI	act_limit_three = 50	[S1 특별약관 제3조(3) <표1>]
Physical-therapy re-assessment gate	First 10 acts unconditional, then 「10회 단위로」 to 50 on documented clinical improvement	physio_gate_acts = 10	[S1] R2
Injection carve-out	항암제, 항생제 (항진균제 포함) and 희귀의약품 leave the ₩2,500,000 sub-limit for the main ₩50,000,000 limit	inject_carve_share	[S1 특별약관 제3조(3)제2항]
Non-NHI branch	Reimbursement falls to 40% of the amount borne, both parts	retain_rate_nonhi = 0.60	[S1 제3조제3항제1호] [S1 특별약관 제3조제8항]
본인부담상한제 exclusion	Amounts refundable ex ante or ex post by the NHIS are excluded from cover	oop_trunc(y)	[S1 제5조제3항] [S1 제4조제3항제1호] R10 REG-R53
요율 상대도 bands	1단계 solved; 2단계 100%; 3단계 200% ≥ ₩1,000,000; 4단계 300% ≥ ₩1,500,000; 5단계 400% ≥ ₩3,000,000	band_thr_3/4/5, reld_r2..r5	[S1 특별약관 제6조제3항] REG-R25
Surcharge floor	No surcharge at all below ₩1,000,000 of prior-year 비급여 claims	band_of()	[S1 특별약관 제6조제4항]
Relativity exemptions	산정특례 conditions, and all claims of an insured graded 장기요양 1·2등급	reld_exempt_share	[S1 특별약관 제6조제3항] REG-R54
Relativity is revenue-neutral	「상대도 적용 전·후의 총 보험료 수준이 일치하도록」 — the discount is solved, not set	reld_solved(y)	[S1]
Relativity base	The rider 순보험료 only; 「비급여 특약 보험료만 할증되며」	prem_gross_mth(y)	[S1] R2
Renewal corridor	±25% a year excluding the age effect, per 위험구분단위, applied to the pre-relativity premium	renewal_corridor = 0.25	[S1 제30조제2항] [S1 특별약관 제6조제2항] REG-R17 제7-63조제2항제3호·제3의2호
무사고 할인	10% of the whole office premium after two consecutive claim-free years	noclaim_disc = 0.10	R1 [S3]
보장내용 변경주기	5 years; re-entry into the generation then on sale, no health underwriting	reentry_period = 5	[S1 제23조] REG-R17 제7-63조제2항제6호나목
Maximum cover age	보험나이 100	max_cover_age = 100	[S3] [S4]
Policy year	「계약일로부터 매1년 단위로 도래하는 계약해당일 전일까지의 기간」	policy_year(t)	[S1 제5조제2항]
Surrender value	Nil	—	[S3]
Death benefit	Nil beyond the 미경과보험료	—	REG-R17 제7-63조제1항제1호 REG-R25 제22조
Indemnity ceiling	「실제 발생한 손해(비용)를 초과하여 보험금을 지급하지 않습니다」	check_indemnity()	[S1 제37조·제38조] [S3]

Two contractual mechanics are specified and implemented but deliberately not exercised by the base run, and both are named rather than hidden. The 3대비급여 gates are hard and neither is pro-rated: the wording works two cases — ₩3,500,000 exhausted after 30 treatments on 2022-10-31 excludes cover for the following 151 days to the 계약해당일 2023-04-01; 50 treatments used with only ₩3,000,000 paid excludes cover for 182 days [S1]. The limit that binds first stops cover for the rest of the policy year and only the anniversary restores it, which makes a 3대비급여 claim stream a censored counting process with an annual reset, not a rate. And the counting rules are asymmetric, each a real modelling instruction [S1 특별약관 제3조(3)제4항]: two or more of the physical-therapy trio at one visit are each counted and each separately deducted; two or more injections at one visit are one act with one deduction; MRI at two sites, or the same site twice, are separate acts each with its own deduction. Read against the ₩30,000 per-act floor, the injection rule is worth money to the insurer and the MRI rule worth money to the insured.

(b) Insurer-discretionary current elements

This class is small, and what is in it is not what a sister library would expect.

Input	Snapshot value	Basis
The rate scale itself	The insurer’s own, unpublished, in the 산출방법서	REG-R2; there is no 실손 참조순보험요율 to fall back on R20
보험가입금액 and per-visit cap menu	Carrier-selected inside the 표준약관’s ceiling; ₩50m/₩30m/₩10m with ₩200k/₩150k/₩100k on a 5세대 menu	[S1 제5조] [S3]; composite takes the maximum std
가입나이 envelope	A 사업방법서 matter, not published; 0–49 on one 2세대 direct product	[S4] REG-R2; composite 0–65 std
Band-1 discount level	Solved from neutrality, not chosen — but the insurer picks the band distribution it solves on	[S1]; std cap at 5%
의료급여 수급권자 할인	5% of office premium at one carrier; not in the composite	[S3]; [std scope]
Basis increment b(y) at renewal	The insurer’s own re-rate, bounded at ±25% per 위험구분단위	[S1 제30조] REG-R17; derived here std, see (c)

What is not discretionary is the striking part. There is no policyholder dividend — the contract is 순수보장성 with no 계약자적립액 to distribute [S3]. There is no 공시이율, no MVA and no non-guaranteed charge scale. And the benefit is not discretionary at all: it is the supervisor’s text, so the whole of what a jplib or uklib product would treat as “current benefit practice” is legislation here. The one genuinely discretionary lever the insurer holds is the price, and even that is bounded by a corridor, verified annually against experience under 감독규정 제7-63조제2항제6호가목, and disclosed at every renewal as a 보험가격지수 under 제7-45조제7항 R12 REG-R17 REG-R22.

(c) Behavioral / experience assumptions (modeler’s view — all std)

Nothing in this subsection is sourced to a rate table, because no rate table for this product exists in public. What the supervisor does publish, annually and in quantity, is aggregate experience R7 R8 R12 REG-R44, and every assumption below is anchored on it and says which anchor it used. Where an anchor bounds the value the bound is given; where none does, that is said.

Mortality. mort_table.csv is a std Makeham construction, q(x) = 1 − exp(−(A + B·c^x)) above age 15 with a log-linear child schedule below it, fitted to the four summary statistics 국가데이터처 publishes — 기대수명 at birth, 기대여명 at 40 and at 65, and survival to age 80 REG-R38. It is not a transcription: 제10회 경험생명표, the industry table applied from 2024-04, is not published in full, and the single-year 완전생명표 qx tables live behind KOSIS and were not downloaded REG-R39. The male fit gives e₀ = 80.585 against a published 80.8, e₄₀ = 42.334 against 41.9, e₆₅ = 19.455 against 19.5 and S(80) = 0.6426 against 0.644; the female fit 86.370 / 47.666 / 23.657 / 0.8215 against 86.6 / 47.4 / 23.7 / 0.822. Parameters: male A = 0.001013180423, B = 1.866071456e-06, c = 1.136151863; female A = 0.0006442732347, B = 9.693652414e-08, c = 1.168822705; child schedule log-linear between q(0) = 0.0025, q(1) = 0.0003, q(5) = 0.0001, q(10) = 0.00008, q(15) = 0.00012; q(110) = 1. Every row carries a provenance column pointing at REG-R38, never at a copy of a table.

The direction of prudence on mortality is inverted here and it matters. On every protection product in this library an understatement of mortality understates the liability. On this one death releases the liability — the contract pays nothing on death beyond the 미경과보험료 — so an over-statement of mortality is anti-conservative. mort_rate_mth(t) = 1 − (1 − q)^(1/12) std, a uniform force across the policy year.

Lapse. lapse_table.csv, annual by policy year, std: 0.100, 0.060, 0.045, 0.035, 0.030, 0.026, 0.024, 0.022, 0.021, 0.020 for policy years 1–10, the last row applying to every later year. No 실손-specific persistency table is published. The ultimate is anchored on the only 실손-specific figure there is — the 1–3세대 in-force block fell 3.3% in 2025 R7 — which blends lapse, death and conversion, so 2.0% is what is left of it once mortality and the renewal decline are taken out. The first-year rate is set against an unverified 장기손해보험 13회차 유지율 of about 86%, from a news summary rather than a retrieved disclosure. lapse_rate_mth(t) = 1 − (1 − w)^(1/12) std. This is non-payment lapse only; the policyholder’s separate right to decline the annual renewal is a different act and carries its own rate.

Renewal decline std. renewal_decline_rate = 0.01 a year, acting only in the twelfth month of each policy year. The asymmetry is contractual: the policyholder may decline renewal and the insurer may not, within the 변경주기 and the age range and provided the prior premium was paid [S5] [S3]. So this is a policyholder option on a contract the insurer cannot exit, and it is the residual of the 3.3% blended decay after lapse and mortality R7. No published 실손 renewal-decline series exists.

Utilisation — the claim frequencies, and what they are frequencies of. utilisation_table.csv carries, per policy per year by sex and five-year age band: adm_rate (admissions), visit_rate_ge and visit_rate_np (outpatient visits on each side), act_rate_physio, act_rate_inject and act_rate_mri (3대비급여 acts), plus los_days, the mean length of stay the room-differential daily-average cap is applied against. These are frequencies of events giving rise to a paid claim, averaged over the whole population including the roughly 65% of insureds who claim nothing in a year R4 R5, which is why they look low against national utilisation.

• The level is solved, not assumed. Three scalars — admissions, 급여 outpatient visits, and everything 비급여 — are chosen so that the anchor cell’s first policy year reproduces the published 4세대 2022 상반기 loss ratios on the published 2021 premium anchor: 급여 97.5% of ₩4,792.80 × 12 and 비급여 73.0% of ₩7,189.20 × 12, i.e. ₩56,075.8 and ₩62,977.4 R12 R1. The model produces ₩56,076.22 and ₩62,978.25. The 비급여 solve additionally needs an inpatient share of the 비급여 claim of 0.30 std, because one admission drives both halves of the claim.

• The age curves and sex factors are shapes std, following the NHIS coverage ratios by age band R9 REG-R41. There is deliberately no maternity bump in the female rows, because pregnancy and childbirth are excluded from 4세대 cover.

• A published grid exists and is not used for the level, and that must be said. 보험개발원’s 장기손해보험 참조순보험요율 display carries a 질병입원율 grid by age and sex REG-R61. It is a 장기손해보험 fixed-benefit hospitalization incidence — an insured-event rate on a 참조순보험요율 (net premium) footing — and not a count of admissions producing a payable indemnity claim after a 20% co-payment; and a reference net rate is not a best estimate. It is therefore available as an external anchor for the age slope of adm_rate and is not used for the level. Substituting it, and restating the level solve against it, is the first thing a user with company data should try. 실손 위험률 itself remains unpublished R20.

Severity — eight discrete distributions, because a mean is unusable here. severity_table.csv gives cost-probability pairs per event for ge_in, ge_out, np_in, np_room, np_out, physio, inject and mri. The reason the shape and not the mean is needed is the deductible: it is max(flat floor, percentage × cost), a flat amount below a crossing point and a percentage above it, so the payment is a kinked function of cost and E[f(X)] ≠ f(E[X]). The dispersion being standardized over is real and published — the 건강보험심사평가원 price survey found 도수치료 quoted anywhere between ₩5,000 and ₩600,000 across Seoul hospitals R2 — and a mean would erase it. Worked example below quantifies the error a mean makes on each stream; on the 비급여 통원 limb it is +35.8%.

The annual-claim shape — the one table whose dispersion is the whole point. claim_shape_table.csv gives the distribution of a policy’s annual rated 비급여 claim across ten buckets as a share and a representative amount. The 요율 상대도 band is decided by where a policy’s annual claim falls against fixed money thresholds, so the band mix is a property of the distribution and not of its average. Bucket 0 carries the 72.9% of contracts assessed with no rated claim R12; the six 2단계 buckets take their within-band dispersion from the six lowest bands of the published 4세대 claim-size distribution — the 0–10만 / 10–20만 / 20–50만 / 50–100만 / 100–200만 / 200–500만 rows at 3.7 / 6.0 / 16.3 / 17.7 / 18.9 / 22.2% of claimants, normalised over themselves and with each band’s midpoint scaled by one common factor onto the sub-₩1,000,000 range 2단계 occupies R12; and the three upper buckets carry the published commencement shares 0.8 / 0.7 / 0.3 R12. The amounts are scaled so that the tabulated mean equals the anchor’s year-1 rated claim, which is what makes the solved band-1 relativity come out at the specification’s 0.9575. The model reads the amounts as multiples of the table’s own mean and rescales them to whatever claim level it is projecting, so the same shape serves every model point and every year. The zero-claim mass is held constant at 0.729012 std — the shape trends its amounts and not its frequency — which is a stated limitation: in reality the frequency of claiming rises with age too and the 1단계 share would fall.

Relativity exemptions. reld_exempt_share = 0.15 std: the share of the rider claim struck out of the rating count for 산정특례 conditions and 장기요양 1·2등급 insureds [S1 특별약관 제6조제3항] REG-R54, anchored on the 15.0% of 2025 claims the supervisor attributes to 암 and 뇌·심혈관질환 R7. The severely ill are exempt from the experience rating, and that is a direct statutory cross-reference between this model and LTC (간병보험) — the only such link in the library.

Cost trends, and the re-rating rule they drive. med_trend_ge = 0.010 and med_trend_np = 0.081 std, from the 국민건강보험공단 진료비 실태조사: in 2024 the scheme’s own outlay grew 4.3%, the statutory co-payment 1.0% and 비급여 8.1% R9 REG-R41. 비급여 is compounding at roughly twice the rate of the whole, and it is the half of the claim with no public price. The re-rating rule follows from them and is itself std: each priced unit is re-rated at its own claim trend, clipped to the corridor,

b_u(y) = clip( med_trend_u × k_trend, −0.25, +0.25 )   for u in {ge, np}

so b(y) is derived and not an input. It keeps each unit’s loss ratio stable against its own cost trend unless the corridor clips it — which is exactly what happens on model point 10.

Age loading. age_load = 0.04 — the only published age-slope datum in any retrieved document, and a derived one. The 표준약관’s five-year renewal illustration prints 나이증가분 of 560, 728, 946, 1,230 and 1,599 against base premiums of 14,000, 18,200, 23,660, 30,758 and 39,985, and each is exactly 4.0% of the previous year’s base [S1 제30조]. It is stylised, at an unnamed age, and it is what the model uses.

Expenses and commission std. The only expense datum retrieved for this product is the aggregate: 손해조사비 plus 사업비 of about ₩2.9조 on ₩18.0조 of 2025 premium — 16.1% — which reconciles with the FSS’s stated break-even 경과손해율 of 「약 85% 수준」 R7. No 상품요약서 with a 사업비 disclosure was obtained for any generation. The split is therefore std and check_expense_split() ties it back to the published total:

Component	Rate	Base	Cells
Commission	6%	office premium	comm_rate
Maintenance expense	7%	office premium	expense_maint_rate
Claim handling	3%	claims, not premium	expense_claim_rate
Total, the published aggregate rounded	16%	office premium	expense_total_rate

The published figure is 16.1%, and the 16% the model carries is that figure rounded std; the three components are a std decomposition of it and none of them is separately published. Two choices inside that table are deliberate. Claim handling is 3% of claims and not of premium, because 손해조사비 is claim-driven and because the experience-rating machinery makes claim frequency a driver of expense as well as of benefit; the two bases coincide at a loss ratio of 100%, which is about where this line has actually run — 101.0% in 2025 R7 — and which is why the aggregate can be read either way. And there is no month-0 acquisition strain at all — a product fact rather than an omission. On a one-year renewable contract renewed on a rolling basis the acquisition/renewal distinction has no content after the first year, so what a sister library books as acquisition expense is carried here as a level commission rate on every premium. 감독규정 제4-32조제5항 caps first-year commission on a 보장성보험 at the first year’s premium and is nowhere near binding at 6% REG-R22.

Two behaviour assumptions with no evidence behind them, both stated as such. physio_cont_prob = 0.60 std is the probability that a physical-therapy course continues past each ten-act clinical re-assessment boundary; this is the only place in krlib where a benefit is gated on a clinical review rather than on a definition, and no observed range is published. And successive years’ claiming is assumed independent std, which is what lets noclaim_share(y) = w₁(y−1) × w₁(y); nothing published gives the persistence of claiming from one year to the next.

Two more std shares that bind nowhere and must still be stated. share_injury = 0.15 splits the raw claim between 상해 and 질병 so that each can be capped at its own ₩50,000,000 limit; and inject_carve_share = 0.25 is the 항암제·항생제·희귀의약품 share leaving the ₩2,500,000 injection sub-limit for the main 비급여 limit. Given that non-covered injections were ₩2.81조, 18.5% of all claims, in 2024 R8, where that boundary is drawn is a first-order calibration question and not a detail.

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Cash flow components and recursions

Notation

Symbol	Meaning	Cells
t	policy month, 0-based: t = 0 … proj_len() − 1	—
proj_len	the number of projected months, the exclusive end of the frame	proj_len()
y, y(t)	policy year, the contractual 1-based label floor(t/12) + 1	policy_year(t)
x, age(t)	가입나이 (만나이); attained age x + floor(t/12)	issue_age(), age(t)
b(y)	lower edge of the five-year utilisation band at age in year y	util_band(y)
l(t)	in-force probability at the start of month t	pols_if(t)
q(t), w(t)	monthly mortality, monthly lapse	mort_rate_mth, lapse_rate_mth
u(t), d_ren(t)	monthly 개인실손 중지 decrement; renewal decline at the year end	suspend_rate_mth, renewal_decline
n_adm, n_ge, n_np	admissions, 급여 통원 visits, 비급여 통원 visits a year	adm_rate, visit_rate_ge, visit_rate_np
a_ph, a_in, a_mr	3대비급여 acts a year: physio trio, injections, MRI	act_rate_*
D(y)	mean length of stay per admission, days	los_days(y)
f_ge(y), f_np(y)	cumulative cost trend from year 1, (1 + m_u·k_trend)^(y−1)	trend_ge, trend_np
r_ge, r_np	자기부담률: 0.20 / 0.30, or 0.60 either side outside NHI	retain_rate_ge/np()
X_j, π_j	severity point and its probability, per stream	sev_points(stream)
μ_S	mean cost of one event of stream S	sev_mean(stream)
C_ge(y)	급여 본인부담금 incurred in year y, before truncation	oop_incurred_ge(y)
S	본인부담상한액 for the model point’s decile	oop_ceiling()
τ(y)	본인부담상한제 truncation factor, min(1, S / C_ge(y))	oop_trunc(y)
Λ	annual limit per 보장종목, Lv per-visit cap	annual_limit(), visit_cap()
σ	상해/질병 split of the raw claim, 0.15	share_injury
g_ge(y), g_np(y)	annual-limit survival factors on the two main limbs	ge_limit_factor, np_limit_factor
C(y)	rated 비급여 claim of year y, exemptions removed	claims_np_rated_pp(y)
ρ_k, π_k	claim-shape bucket k’s amount as a multiple of the shape mean, and its share	shape_rel(k), shape_share(k)
w_b(y), r_b	band share and band relativity at the renewal opening year y	band_share(y,b), band_relativity(b)
Σ(y)	surcharge pool, Σ_{b≥2} w_b r_b	reld_surcharge(y)
r₁(y), R(y)	band-1 relativity after the cap; average relativity applied	reld_one(y), reld_avg(y)
nc(y)	share of contracts earning the 무사고 할인	noclaim_share(y)
a	age loading at renewal, 0.04	age_load
b_ge(y), b_np(y)	basis increments, each clipped to ±0.25	basis_incr_ge/np(y)
G_ge(y), G_np(y)	the two 기준보험료 a month	prem_ge_base, prem_np_base
G(y)	office premium a month	prem_gross_mth(y)

Dimensional check, and the error it catches. n_adm, n_ge, n_np, a_ph, a_in, a_mr are events per policy-year; q, w, u, d_ren, π_j, π_k, τ, g and every r, w_b, R are dimensionless; D is days; X_j, μ_S, C_ge, S, Λ, Lv, C, G are KRW; room_cap_day is KRW/day, so room_cap_day × D is KRW per admission. n_adm × μ_ge_in is KRW per policy-year and dividing by 12 gives KRW per policy-month. The error this catches is the one an actuary arriving from a fixed-benefit health product makes without noticing: there is no benefit amount to multiply by. A rate times a 보험가입금액 has the dimensions of money but is not this contract’s claim, and any formula in which annual_limit() appears as a multiplier rather than inside a min is wrong by construction.

The reimbursement machinery, in the order it must be applied

Everything in this product is a rule for reducing an incurred cost to a payable amount, and the order matters. The supervisor’s own identity — 「실손의료보험은 피보험자(환자)가 부담하여 실제 발생한 의료비[급여 본인부담금 + 비급여] 중 일정 금액을 보상하는 보험상품」 R7 — fixes what goes in; five steps fix what comes out.

Step 1 — 본인부담상한제 first, as an exclusion from covered loss.

C_ge(y) = ( n_adm(y)·μ_ge_in + n_ge(y)·μ_ge_out ) · f_ge(y)
τ(y)    = min( 1, S / C_ge(y) )        ( ≡ 1 where nhi_covered = 0 )

and τ(y) multiplies both 급여 limbs and the 급여 half of the incurred covered loss. 국민건강보험법 제44조제2항 creates the scheme and the NHIS refunds the excess of a member’s annual 본인일부부담금 over the ceiling REG-R53, operated as 사전급여 and 사후환급 R10; the 표준약관 then excludes the refundable amount twice over, at 제5조제3항 and at 제4조제3항제1호 [S1]. So the 급여 half of the claim is bounded above, per insured per year, at roughly 0.80 × S — ₩720,000 for a 1분위 insured on the 2026 scale and ₩6,744,000 for a 10분위 one.

Two refinements are deliberate simplifications and are marked. The two years do not align: the policy year runs from the 계약해당일 [S1 제5조제2항] while the 본인부담상한제 runs 1 January to 31 December R10, and this model does not attempt to reconcile the clocks. And a proportional truncation of an expectation is not the same thing as truncating each realisation — E[min(X, S)] ≠ min(E[X], S) — so τ understates the truncation’s bite for exactly the reason a limit applied to a mean understates a limit’s. Where it is switched off entirely (nhi_covered = 0) that is not a simplification but the product: a life outside the scheme is not refunded by it, so oop_ceiling() returns infinity.

Step 2 — the co-payment and the deductible, per event, never on a mean.

Inpatient, both sides, is a flat percentage:

paid_ge_in(y) = n_adm(y)·μ_ge_in·f_ge(y)·τ(y)·(1 − r_ge)  +  top_up(y)
top_up(y)     = max( 0, n_adm(y)·μ_ge_in·f_ge(y)·τ(y)·r_ge − 2,000,000 )
paid_np_in(y) = n_adm(y)·[ μ_np_in·f_np(y)·(1 − r_np)
                           + Σ_j π_j · min( 0.50·X_j·f_np(y), 100,000·D(y) ) ]

The 상급병실료 term is the one place a length of stay enters this model, and it enters because the ₩100,000 cap is applied to the daily average — total non-covered room charge divided by total days — and not night by night [S1 특별약관 제3조]. A single expensive night inside a long stay is therefore smoothed against the stay length rather than capped, a materially more generous treatment than a nightly cap.

Outpatient, both sides, is a kinked function of cost and the expectation must be taken over the distribution:

e(S, φ, r, f) = Σ_j π_j · min( max( 0, X_j·f − max(φ, r·X_j·f) ), Lv )

paid_ge_out(y) = n_ge(y) · [ κ·e(ge_out, 10,000, r_ge, f_ge(y)·τ(y))
                             + (1−κ)·e(ge_out, 20,000, r_ge, f_ge(y)·τ(y)) ]
paid_np_out(y) = min(n_np(y), 100) · e(np_out, 30,000, r_np, f_np(y))
                 + carve(y)

with κ = clinic_share(). The shape matters more than the formula. The deductible is a flat floor that becomes a percentage: at the 급여 clinic tier ₩10,000 until the covered cost reaches ₩50,000 and 20% above it; at the hospital tier ₩20,000 until ₩100,000; on the 비급여 side a flat ₩30,000 until ₩100,000 and 30% above it. So a ₩10,000 clinic visit pays nothing, a ₩50,000 visit pays ₩40,000, and above the crossing point the payment is a straight percentage of cost until the ₩200,000 per-visit cap binds — at a covered cost of ₩250,000 on the 급여 side, the same crossing point at both provider tiers. 4세대 merged 외래 and 처방조제 into one visit with one deductible where 3세대 carried a separate ₩8,000 처방조제 deductible on top [S1] [S5], which is why a 3세대 frequency basis cannot be carried across without adjustment; the visit counts here are counts of merged visits std.

Step 3 — the ₩2,000,000 annual inpatient co-payment cap, on the retention that survives step 1. Written into paid_ge_in above as top_up(y). It applies to inpatient treatment only; there is no annual cap on the outpatient deductible. Both this and the 본인부담상한제 reduce the insured’s retention on heavy 급여 use, which is precisely why the order is fixed: the ceiling first as an exclusion from covered loss, the ₩2,000,000 cap second on what remains. Applying them in the other order, or in parallel, double-counts the relief.

Step 4 — the 3대비급여 sub-limits, which displace the main limit for their three classes. Per act there is no visit cap, only the ₩30,000 floor:

p(S, f) = Σ_j π_j · max( 0, X_j·f − max(30,000, r_np·X_j·f) )

a_ph_eff(y) = min(a_ph(y), 50) capped at 10, plus 0.60 × the excess over 10
a_in_eff(y) = min(a_in(y), 50) × (1 − 0.25)
carve(y)    = min(a_in(y), 50) × 0.25 × p(inject, f_np(y))

claims_physio(y) = min( a_ph_eff(y)·p(physio, f_np(y)), 3,500,000 )
claims_inject(y) = min( a_in_eff(y)·p(inject, f_np(y)), 2,500,000 )
claims_mri(y)    = min( a_mr(y)·p(mri, f_np(y)),        3,000,000 )

Four contractual facts are in those five lines. The physical-therapy trio — 도수치료, 체외충격파치료, 증식치료 — share one 50-act counter and one money limit, so they are one frequency here [S1 특별약관 제3조(3) <표1>]. Cover beyond the first ten acts is conditional on a documented clinical re-assessment at each ten-act boundary, on a named test set — 관절가동(ROM), 통증평가척도, 자세평가 및 근력검사(MMT), 초음파 검사 — with the insurer bearing the whole cost of the assessment [S1] R2; a projection can only represent that as a continuation probability, and 0.60 is std. The injection carve-out moves the 항암제·항생제·희귀의약품 share out of the ₩2,500,000 sub-limit and into the main ₩50,000,000 비급여 limit [S1 특별약관 제3조(3)제2항], so the acts are removed from a_in_eff and their payment added to paid_np_out — counted once, in exactly one place. And MRI has a money limit and no act counter at all, the only one of the three without one.

Step 5 — the annual aggregates, per 보장종목 and per policy year. 상해 and 질병 carry separate ₩50,000,000 limits on each of the two parts [S1 제5조]:

raw    = paid_in + paid_out                    (each side separately)
capped = min(σ·raw, Λ) + min((1−σ)·raw, Λ)
g(y)   = capped / raw

and g_ge(y), g_np(y) are applied back to the printed limbs so that the five result_cf() columns still sum to the limited total. The 3대비급여 limbs never pass through g_np — they are already at their own sub-limits, which replace the aggregate rather than sitting inside it. Where 3대비급여형 is not held those treatments are not covered at all rather than falling back into the main limit.

A necessary honesty about every limit in step 5, and about the counters in step 4. On a deterministic expected-value grid E[min(X, Λ)] ≠ min(E[X], Λ), so a projection that applies a limit to an expectation understates the limit’s bite by ignoring dispersion. On every shipped model point the ₩2,000,000 inpatient cap, the three 3대비급여 money limits, the two 50-act counters, the 100-visit cap and the four ₩50,000,000 aggregates do not bind, because the expected annual claim of a single cell is two orders of magnitude below them — the supervisor’s own tail figure is that 0.005% of insureds took more than ₩50,000,000 in 2019 R1. The machinery is implemented anyway, because it binds under any seriatim or stochastic run and because check_annual_limits() is what proves it is wired correctly. check_annual_limits() returning True says the limits are wired, not that they are exercised. Do not delete a limit because it reads slack. The one limit that does bind on a shipped model point is the 본인부담상한제 truncation, on model point 8.

The indemnity ceiling, which is this product’s defining constraint and no other’s.

loss_incurred(y) = C_ge(y)·τ(y)
                 + n_adm(y)·(μ_np_in + μ_np_room)·f_np(y)
                 + n_np(y)·μ_np_out·f_np(y)
                 + ( a_ph(y)·μ_physio + a_in(y)·μ_inject + a_mr(y)·μ_mri )·f_np(y)

claims_ann(y) ≤ loss_incurred(y)                              [check_indemnity]

「동일한 위험을 보장하는 2개 이상의 계약에 중복 가입 하더라도 실제 발생한 손해(비용)를 초과하여 보험금을 지급하지 않습니다」 [S1 제37조·제38조] [S3]. A co-payment applied as a multiplier instead of a retention, a deductible subtracted twice, or a per-visit cap applied to the wrong side of the deduction would all show up here, and nowhere else. Cancer_KR_S and LTC_KR_S have no analogue of this check because they have no incurred loss to bound against — it is the 정액 / 실손해 fork of 감독규정 제7-63조제1항제2호 in one identity REG-R17.

The premium recursion and its corridor

G_ge(y) = G_ge(y−1) · (1 + a) · (1 + b_ge(y)),     G_ge(1) = (1 − s)·P₀
G_np(y) = G_np(y−1) · (1 + a) · (1 + b_np(y)),     G_np(1) = s·P₀
G(y)    = [ G_ge(y) + G_np(y)·R(y) ] · ( 1 − 0.10·nc(y) )

The order of operations is the thing a careless reading gets wrong, and the 표준약관’s own illustration settles it. Its column label reads 「기초율 증가분 = 전년도 기준보험료 × 25%」, but 3,640 is 25% of 14,560 = 14,000 × 1.04, not of 14,000 [S1 제30조]. So the corridor applies to the age-adjusted prior premium, and only the recursion above reproduces the illustration’s printed row 14,000 → 18,200 → 23,660 → 30,758 → 39,985 → 51,980. Getting it wrong costs 4% of the corridor every year and compounds: on this model’s 비급여 unit the correct annual factor is 1.04 × 1.081 = 1.12424 and the additive misreading gives 1.121, which puts the year-10 rider base premium 2.564% low — ₩20,096.9929 against ₩20,625.8505.

Three further points, each sourced. The corridor binds per 위험구분단위, not on the portfolio average [S1 제30조제2항] REG-R17 제7-63조제2항제3호, which is why the two units are clipped separately and check_renewal_corridor() tests each. It applies to the pre-relativity premium — 「요율 상대도 적용 전 보험료」 [S1 특별약관 제6조제2항] REG-R17 제7-63조제2항제3의2호 — so a band-5 policyholder can face 1.25 × 4.00 = 5.00× the previous year’s base rider rate in a single step, which is the sharpest number in the product. And the relativity applies to the 순보험료 (「특별약관의 순보험료 총액을 대상으로 합니다」 [S1]); this model applies it to the rider’s office premium and re-grosses at the same expense ratio, which is arithmetically identical std and would fail only if the rider’s expense loading contained a fixed per-policy amount, which no retrieved document states either way.

The composition reproduces the wording’s own five-band table. At s = 0.4875 — the share implied by solving the illustration’s own band-2 and band-5 rows — the formula gives 18,200 × (0.5125 + 0.4875 × 2) = 27,073 at renewal +1 and 23,660 × (0.5125 + 0.4875 × 4) = 58,263 at +2, reproducing [S1]’s printed 27,073 and 58,263 to the won — the raw products are 27,072.5 and 58,262.75, and the wording’s table is printed rounded. That reproduction is the check that the composition is the right one. The model itself runs at s = 0.60, from R2.

비급여 할인·할증 — the loop, written out

This is the mechanism that makes the contract unlike anything else in this repository: the renewal premium of the 비급여 rider is a function of the individual policyholder’s own prior-year non-covered claim amount. It is a feedback loop from claims to premium, inside a single policy, on an annual clock.

C(y)        = (1 − 0.15) · claims_np(y)                       [exemptions removed]
band(A)     = 1 if A ≤ 0; 2 if A < 1,000,000; 3 if A < 1,500,000;
              4 if A < 3,000,000; 5 otherwise
w_b(y)      = Σ_k π_k · 1{ band( ρ_k · C(y−1) ) = b },        w_b(1) = 1{b = 2}
Σ(y)        = Σ_{b≥2} w_b(y) · r_b                            r = (1, 2, 3, 4)
r₁*(y)      = ( 1 − Σ(y) ) / w₁(y)                            [revenue neutrality]
r₁(y)       = max( r₁*(y), 0.95 )                             [the [std] 5% cap]
R(y)        = w₁(y)·r₁(y) + Σ(y)      if the relativity is live, else 1
nc(y)       = w₁(y−1) · w₁(y)         for y ≥ 3, else 0

Six things in those seven lines are load-bearing and each is sourced or flagged.

1. The discount is solved, not set. 「매년 상대도 적용 전·후의 총 보험료 수준이 일치하도록 3~5단계의 할증대상자의 할증재원을 1단계(할인) 대상자들에게 분배할 경우 산출됨」 [S1]. The scheme is revenue-neutral within the rider: the surcharge funds the discount and the insurer collects the same rider net premium either way. On the commencement band distribution 72.9 / 25.3 / 0.8 / 0.7 / 0.3 R12 that gives Σ = 0.301988 and r₁* = 0.698012 / 0.729012 = 0.9574767, a 4.2523% discount — the specification’s 0.9575, produced as a result rather than typed in. The published values bracket it and one lies outside: 「5% 내외」 at launch R1, −5% 잠정 at commencement R3, a 95% relativity in the wording’s own illustration [S1], and one carrier writing it as 「α%」 rather than a number [S3]. On the FSC’s alternative commencement distribution 62.1 / 36.6 / 1.3 R3 the same identity gives 0.9791, a discount of only 2.1% — the sensitivity is material, which is why both distributions are recorded rather than averaged. Solving rather than hard-coding means a change in the band distribution propagates correctly instead of silently breaking neutrality, and check_relativity_neutral() is the identity that proves it.

2. The 5% cap is std and it eventually binds. reld_disc_cap = 0.05 is a floor under the discount taken from the two published values R1 R3. It does not bind at commencement, where the solved figure is 4.25%. It binds once the claim level has trended far enough that contracts migrate into the surcharge bands and the pool would fund more than 5% — at which point the scheme stops being revenue-neutral and the average rider premium rises above the base. That is the loop reaching the aggregate, and it is a feature of the design rather than of this implementation.

3. The thresholds are fixed money amounts and the claim level trends, so contracts migrate into the surcharge bands year after year with nothing in the model changing. That migration is the loop, and it is why the band mix must be recomputed every year rather than fixed at the commencement distribution.

4. The lookback window. 「보험료 갱신 전 12개월 이내 기간」 [S1 특별약관 제6조제3항], with an operational three-month offset because renewal notices go out about a month ahead — 「계약해당일이 속한 달의 3개월 전 말일부터 직전 1년간」 R12 — which 5세대 writes into the standard text [S2]. On an annual grid the offset is invisible; on a model that tried to resolve it the point would be that a claims-to-renewal lag of zero over-states the responsiveness of the loop.

5. The relativity was deferred three years. The clause was in the wording from launch and its application commenced 2024-07-01 「충분한 통계 확보 등을 위하여」 R3 R1, so a 4세대 policy written in 2021 had three renewals at flat relativity before the loop switched on. reld_start_year = 4. The same deferral is being repeated on 5세대, whose differential starts 2028-05-06 [S3].

6. The 무사고 할인 runs alongside and is a different animal. 「직전 2년간 비급여 보험금(4대 중증질환 치료를 위한 보험금은 제외) 미수령시 차기 1년간 보험료(급여(주계약)

   • 비급여(특약))의 10%를 할인」 R1. It has a two-year lookback where the relativity has one; it applies to the whole office premium where the relativity touches only the rider; and it stacks with the band-1 discount. The launch release prints a three-year timeline in which years 1 and 2 give only the rider discount and year 3 adds the 10% R1. The model reproduces the 10% leg of that timeline exactly — nc(y) is zero in years 1 and 2 and 0.5314584961 from year 3 — and deliberately not the other leg: the rider discount was deferred to 2024-07-01 R3, so on the modelled generation years 1 to 3 carry no relativity at all (reld_start_year = 4).

Decrement recursion and processing order

For t = 0, 1, …, proj_len() − 1:

1. Start of month. premiums(t) = G(y(t)) · l(t).

2. Look up the annual basis. age(t), hence util_band(y) and every frequency; hence f_ge(y), f_np(y), τ(y) and the whole of the five-step machinery above, computed once per policy year and divided by twelve.

3. End of month — claims and expenses.

   claims(t, kind) = l(t) · claims_ann_pp(y(t), kind) / 12
   expenses(t)       = 0.07 · premiums(t)
   claim_expenses(t) = 0.03 · claims(t)
   commissions(t)    = 0.06 · premiums(t)
   

4. End of month — decrements, in order.

   l_1 = l(t) · (1 − q(t))                          mortality
   l_2 = l_1  · (1 − w(t))                          lapse
   l_3 = l_2  · (1 − u(t))                          개인실손 중지
   l(t+1) = l_3 · (1 − d_ren(t))                    renewal decline, year end only
   

   exposed as pols_if_at(t, timing) at BEF_DECR / BEF_LAPSE / BEF_SUSPEND / BEF_RENEWAL / AFT_DECR, with the five decrement counts pols_death, pols_lapse, pols_suspend, pols_renewal_decline and pols_maturity taken at the matching points. d_ren(t) is non-zero only where (t + 1) mod 12 = 0; pols_maturity(t) is non-zero only at t = proj_len() − 1, where it absorbs everyone left. Lapse and death both pay nothing.

Five decrements, and the middle three are what make this roll-forward different from a term assurance’s. 개인실손 중지 is a supervisory requirement rather than a product feature REG-R17 제7-63조제2항제7호; the renewal decline is an option the policyholder holds and the insurer does not; and the maturity count is the stated horizon rather than the end of cover. Without all three the roll-forward would appear to lose lives with no cause, and check_pols_roll_fwd() would fail.

Net cash flow

net_cf(t) = premiums(t) − claims(t) − expenses(t)
                         − claim_expenses(t) − commissions(t)

income-positive, with claims(t) the sum of the five limbs GE_IN, GE_OUT, NP_IN, NP_OUT, NP_THREE. result_cf() publishes the five limbs as separate columns and deliberately no claims subtotal column, so that the printed columns sum to net_cf and a limb cannot be double-counted invisibly; the claims(t, kind) cells stays. expenses is maintenance only and the claim-handling expense stands beside it in its own claim_expenses column, which is what the two names mean library-wide and which keeps a premium-driven cost and a claim-driven cost from moving together in one figure.

Because every rate in the ledger is proportional, the whole cash flow collapses to a two-term identity that is worth writing down, since it governs everything the Worked example shows:

net_cf(t) = 0.87 · premiums(t) − 1.03 · claims(t)

so the sign of net_cf in any period is decided by a single number, the loss ratio, against

LR* = 0.87 / 1.03 = 0.8446601942

The model’s own break-even loss ratio is 84.47%, which sits just below the FSS’s stated break-even of 「약 85% 수준」 R7. The gap is the expense loading, not the basis the claim handling is charged on: at that loss ratio the 3% of claims is 2.53% of premium, so the model is carrying 6 + 7 + 2.53 = 15.53% of premium against the 15% residual an 85% break-even implies. Charging the claim handling on premium instead would take the model’s break-even down to 84.00%, not up — the claims basis narrows the gap rather than causing it.

Optional modules (all off, or neutral, in the base run)

Module	Base-run setting	What switching it on does
개인실손 중지	suspend_rate = 0	A fourth decrement at 1 − (1 − r)^(1/12) a month. Mandatory as a facility REG-R17 제7-63조제2항제7호 R16 [S3]; carried as a decrement and not as a state, because the contract that resumes is a different projection. Model point 9 carries 3% a year.
The 40% branch	nhi_covered = 1	Raises r_ge and r_np to 0.60 and switches the 본인부담상한제 off. Model point 10.
Cost-trend stress	trend_mult = 1.0	Multiplies both med_trend_*. At 4.5 the 비급여 re-rate would be 36.45% and the corridor clips it to 25%; model point 10.
Utilisation stress	util_mult = 1.0	Multiplies every frequency. Model point 8 carries 10.0 — a cell inside the top claim decile — and is the only shipped point where the public truncation binds.
요율 상대도 off	reld_on = 1	With it off the contract is a plain attained-age renewable, which is what 1세대 through 3세대 were. Model points 5 and 9.
무사고 할인 off	noclaim_on = 1	Model points 5 and 9.
비급여 특약 off	np_rider = 1	Removes 60% of the premium, the 100-visit cap, the three sub-limits and the whole loop. Model point 5.
3대비급여형 off	three_np = 1	Those treatments become uncovered, not reassigned to the main limit. Model point 6.
Lower 보험가입금액 rung	annual_limit = 50m, visit_cap = 200k	Model point 7 at ₩10,000,000 / ₩100,000.

Two things are not modules and are not modelled at all, and both are limitations rather than omissions. The 재가입 terms change: the model assumes re-entry on unchanged terms at t = 60, so nothing whatever happens in the cash flows at the first 보장내용 변경주기, and that no-op is the assumption made visible. A 5세대 re-entry would change the partition, the 비중증 co-payment and the limits at once — see the delta table in product-spec.md. And the behavioural response to the experience rating: the supervisor’s own worked example has a policyholder cutting his claims by 93% in response to a surcharge, from ₩10,000,000 to ₩700,000, saving ₩300,000 of premium and ₩2,700,000 out of pocket in one year R2. The contract is designed to change the insured’s behaviour, and this model projects the premium’s response to claims but not the claims’ response to premium.

---

Policyholder behavior modeling

• Lapse is real, immediate and unbroken. There is no surrender value, so there is no 보험료 자동대출납입 to advance a missed premium and no 보험계약대출 to lend against — 표준약관 제33조 excludes 「순수보장성보험 등」 from policy lending in terms REG-R25. A missed premium produces a 납입최고 of at least 14 days and the contract terminates the day after it ends REG-R25 제26조. So no lapse-suppression term belongs in the recursion, and claims_lapse is identically zero. This is the structural fork between the 실손 chassis and the whole life savings chassis (종신보험), whose 자동대출납입 and 보험계약대출 machinery must not be imported here.

• Declining the renewal is a different act from lapsing, and the contract says so. The policyholder may decline the annual renewal; the insurer may not [S5] [S3]. renewal_decline is therefore a decrement of its own, non-zero only in the twelfth month of a policy year, and it is the decrement this product is genuinely exposed to: on a one-year contract that re-rates every year at the attained age, the renewal is where the policyholder actually makes a decision. Folding it into lapse_rate would make the annual boundary invisible.

• The re-entry decision is not modelled as a decrement at all. At the fifth 계약해당일 the policyholder may take whichever 실손 product the company is then selling, and 「회사는 이를 거절할 수 없습니다」 [S1 제23조제2항] R2. Where the decision cannot be obtained the contract is extended on the previous terms [제5항], the policyholder may cancel that extension within 90 days with a full refund of premium paid after it [제6항], and the extension runs until intention is established — typically the date of the first claim [제7항], capped at one year from the end of the 보험기간 at one carrier [S3 제53조제7항]. None of that is a cash flow this model can produce without a new-business funnel, so t = 60 carries the ordinary 1% renewal decline and nothing more std. A re-entry into a materially different generation would plausibly carry a higher decline, and that is a named sensitivity rather than a modelled effect.

• Suspension is not lapse either. A policyholder covered by a 단체실손 may suspend the individual policy for the duration and resume it within one month of the group cover ending R16 [S3], and the facility is mandatory REG-R17 제7-63조제2항제7호. The resumed contract must match on four attributes to count as the same — 보장종목, 보험가입금액, 자기부담금, 최대 보장가능 보험나이 [S3] — which is precisely why resumption is not modelled: the contract that resumes is a different projection, entering the product in force at resumption. Suspension here ends the cash flows and nothing more.

• Duplicate cover buys nothing, and that is a behavioural fact about the population rather than about the cell. 「동일한 위험을 보장하는 2개 이상의 계약에 중복 가입 하더라도 실제 발생한 손해(비용)를 초과하여 보험금을 지급하지 않습니다. (중복 가입 시 비례보상)」 [S3], under 표준약관 제37조·제38조. It is why 36.22 million policies can cover about 40 million insureds without either number being wrong R7 R4, and it is a thing a fixed-sum contract could not do. A single-policy projection is unaffected; a portfolio model that scaled claims by policy count rather than by insured count would double-count.

• No dynamic lapse from a cash value or an interest rate. There is no 해약환급금, no 공시이율, no 예정이율 disclosure on a one-year contract and no MVA, so there is no economic surrender trigger to model. Neither the 무해지환급형 surrender-value cliff at 납입완료 nor the 유지보너스-date lapse spike that whole life wires to its persistency bonus has any analogue here.

• Anti-selective lapse is not modelled, and the direction is the reverse of a term product’s. Healthy lives decline renewal first, so the persisting block is progressively impaired on the morbidity basis. The natural form, freq_eff(y) = freq(y) × [1 + λ·max(0, cumulative exits − ref)], is not implemented and λ = 0 is the base run: no Korean 실손 selective-lapse evidence was retrieved. But the experience rating makes this product’s version of the effect much sharper than a term product’s, because the surcharge is itself a signal — a policyholder facing a 300% relativity is a policyholder the model has already identified as a heavy claimant, and whether he renews at all is exactly the question λ would answer.

• The behavioural response to the surcharge is the elephant, and it is not modelled. The FSC/FSS FAQ works the design’s intended case in full: a 45-year-old male paying ₩5,000 급여 plus ₩8,000 비급여 takes about 20 sessions of 도수치료 at ₩500,000 a session, claims ₩10,000,000 and receives ₩7,000,000; his rider premium quadruples to about ₩32,000 and his total to about ₩40,000; he then shops on the 심평원 price disclosure, cuts his claims to ₩700,000, and his rider premium resets to about ₩9,000 including the age increment — a saving of ₩300,000 in premium and ₩2,700,000 out of pocket in one year R2. The contract is designed to change the insured’s behaviour, and Medical_KR_S models the premium’s response to claims and not the claims’ response to premium. Stated as a limitation, and it is the single largest one in this document.

• Elections are not behaviour. 보장종목, 보험가입금액 and the per-visit cap are chosen at issue and are model point attributes; nothing in the projection may vary them over t. The one thing that can change them is 재가입, and that is a scheduled terms change at a contractual date, not a policyholder decision the model is entitled to simulate.

• 청약철회 is out of scope. 15 days from receipt of the 보험증권 or 30 days from application, whichever comes first, effective on despatch REG-R51; it is a pre-inception decrement and modelling it would need a new-business funnel this library does not have.

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Worked example

Everything in this section is read off the shipped model, not recomputed by hand. The test module asserts it cell by cell at the precision displayed.

The anchor cell

point_id = 1 — 남자, 만나이 40 at issue, all five 보장종목 held (상해급여형 and 질병급여형 in the 주계약; 상해비급여형, 질병비급여형 and 3대비급여형 in the 특약), 연간 보험가입금액 ₩50,000,000 per 보장종목, 통원 1회당 ₩200,000, 월납 office premium ₩11,982 in the first policy year, split 급여 ₩4,792.80 / 비급여 ₩7,189.20 at s = 0.60. 본인부담상한제 decile 6 (ceiling ₩3,260,000 on the 2026 scale), 급여 통원 clinic-tier share 0.63, inside 국민건강보험. Both the 요율 상대도 and the 무사고 할인 are switched on; trend_mult = util_mult = 1.0; suspend_rate = 0.

proj_len() = 120, so result_cf() has 120 rows, t = 0 … 119 — ten policy years, two five-year 보장내용 변경주기, ending in the twelfth month of policy year 10 at attained 만나이 49. pols_if_init() = 1.0.

The ₩11,982 is not an assumption of this document; it is the published new-business anchor for exactly this cell — 40세 남자, 4세대, 10-carrier 손해보험 average, 2021-06 R1 — and age 40 male is the 기준연령 요건 of 감독규정 제1-2조제2호 REG-R9.

Every assumption value the anchor cell uses

Frequencies — utilisation_table.csv, per policy per year, all std. The anchor reads (M, 40) in policy years 1–5 and (M, 45) in years 6–10.

Band	adm_rate	los_days	visit_rate_ge	visit_rate_np	act_rate_physio	act_rate_inject	act_rate_mri
M, 40	0.014140	7.500000	1.885433	0.236694	0.092047	0.078898	0.015780
M, 45	0.017674	8.250000	2.224811	0.279298	0.112298	0.096255	0.020198
ratio	1.2499293	1.100000	1.1800000	1.1799961	1.2200072	1.2199929	1.2799747

Severities — severity_table.csv, all std, with the expected payment per event at trend 1.0, which is what policy year 1 uses. The right-hand column is where the shape earns its place: it is not any simple function of the mean.

Stream	(cost, probability) points	mean μ_S	expected payment per event, year 1
ge_in	(250,000, .40) (700,000, .32) (1,800,000, .20) (5,000,000, .07) (15,000,000, .01)	1,184,000	947,200 = 0.80 × mean (flat percentage)
ge_out	(8,000, .30) (18,000, .30) (40,000, .25) (90,000, .12) (250,000, .03)	36,100	clinic tier 24,540; hospital tier 19,400; blend at κ = 0.63 → 22,638.20
np_in	(400,000, .40) (1,200,000, .33) (3,000,000, .20) (8,000,000, .07)	1,716,000	1,201,200 = 0.70 × mean
np_room	(0, .55) (300,000, .30) (1,200,000, .15)	270,000	135,000 at D = 7.5 (daily-average cap ₩750,000 a stay)
np_out	(45,000, .35) (90,000, .30) (180,000, .22) (400,000, .10) (900,000, .03)	149,350	76,970
physio	(80,000, .35) (120,000, .35) (180,000, .22) (400,000, .08)	141,600	97,020 per act
inject	(60,000, .40) (120,000, .30) (250,000, .20) (700,000, .10)	180,000	121,200 per act
mri	(450,000, .45) (700,000, .35) (1,100,000, .20)	667,500	467,250 per act

Claim shape — claim_shape_table.csv, shape_mean() = 53,530.7923920000. The last two columns are the rescaling in action: the amounts are read as multiples of the table’s own mean and rescaled to the year’s rated claim.

bucket	claim_amount	share	shape_rel	amount at C(1)	band at the year-2 renewal
0	0	0.729012	0.0000000000	0.00	1단계
1	2,184	0.011039	0.0407989477	2,184.03	2단계
2	6,551	0.017901	0.1223781623	6,551.09	2단계
3	15,285	0.048628	0.2855365915	15,285.21	2단계
4	32,753	0.052805	0.6118534499	32,753.44	2단계
5	65,506	0.056385	1.2237068998	65,506.88	2단계
6	152,847	0.066230	2.8553098725	152,849.05	2단계
7	1,200,000	0.008000	22.4170042396	1,200,016.10	3단계 (→ 4단계 from y = 5)
8	2,000,000	0.007000	37.3616737326	2,000,026.83	4단계 (→ 5단계 from y = 7)
9	4,500,000	0.003000	84.0637658985	4,500,060.37	5단계

Decrements. mort_table.csv std Makeham, male: q(40) = 0.00132019, q(41) = 0.00136205, q(44) = 0.00152503, q(45) = 0.00159477, q(49) = 0.00198242; mort_rate_mth(0) = 1 − (1 − 0.00132019)^(1/12) = 0.0001100825. lapse_table.csv std: 0.100 in policy year 1 falling to 0.020 by year 10, so lapse_rate_mth(0) = 1 − (1 − 0.10)^(1/12) = 0.0087416110 and lapse_rate_mth(12) = 1 − (1 − 0.06)^(1/12) = 0.0051430128. renewal_decline_rate = 0.01, acting at t = 11, 23, …, 119. suspend_rate = 0.

본인부담상한액. oop_ceiling_table.csv, 2026 scale R10: 900,000 / 1,120,000 / 1,120,000 / 1,730,000 / 1,730,000 / 3,260,000 / 3,260,000 / 4,460,000 / 5,360,000 / 8,430,000 for deciles 1–10. The anchor is decile 6, ceiling ₩3,260,000, against an incurred 급여 본인부담금 of ₩84,805.8913 in policy year 1 — headroom of a factor of 38.4 — so `oop_trunc(y) = 1.0 throughout on this cell. The truncation binds on model point 8 and nowhere else.

Scalar References, in full. reentry_period 5, reentry_cycles 2, max_cover_age 100, renewal_decline_rate 0.01, retain_rate_ge_base 0.20, retain_rate_np_base 0.30, retain_rate_nonhi 0.60, ded_clinic 10,000, ded_hospital 20,000, ded_np_out 30,000, cap_inpatient_retain 2,000,000, room_rate 0.50, room_cap_day 100,000, visit_limit_np 100, act_limit_three 50, physio_gate_acts 10, physio_cont_prob 0.60, limit_physio 3,500,000, limit_inject 2,500,000, limit_mri 3,000,000, inject_carve_share 0.25, share_injury 0.15, med_trend_ge 0.010, med_trend_np 0.081, age_load 0.04, renewal_corridor 0.25, band_thr_3/4/5 1,000,000 / 1,500,000 / 3,000,000, reld_r2..r5 1 / 2 / 3 / 4, reld_disc_cap 0.05, reld_start_year 4, reld_exempt_share 0.15, noclaim_disc 0.10, comm_rate 0.06, expense_maint_rate 0.07, expense_claim_rate 0.03, expense_total_rate 0.16, roll_fwd_tol 1e-10, cash_tol 1e-06, shape_tol 1e-09.

The calibration closing. Policy year 1 gives a 급여 loss ratio of 0.9750080 and a 비급여 loss ratio of 0.7300099 against published 4세대 2022 상반기 figures of 97.5% and 73.0%, and a combined 0.8280091 against the published 82.8% R12. That is the solve, and it is the reason the frequency level is what it is.

The cash flow statement, policy year 1

Per policy issued, income-positive, pols_if to ten decimals and cash to ₩0.0001 — the precision the tests assert. Within a policy year every per-policy quantity is constant, so every row below is row t = 0 scaled by pols_if(t); the whole of policy year 1 is one set of rates.

t	pols_if	premiums	claims_ge_in	claims_ge_out	claims_np_in	claims_np_out	claims_np_three	expenses	claim_expenses	commissions	net_cf
0	1.0000000000	11,982.0000	1,116.1173	3,556.9008	1,574.4890	1,717.4122	1,956.2861	838.7400	297.6362	718.9200	205.4984
1	0.9911492689	11,875.9505	1,106.2389	3,525.4196	1,560.5536	1,702.2119	1,938.9715	831.3165	295.0019	712.5570	203.6796
2	0.9823768732	11,770.8397	1,096.4479	3,494.2171	1,546.7416	1,687.1460	1,921.8102	823.9588	292.3909	706.2504	201.8769
3	0.9736821197	11,666.6592	1,086.7435	3,463.2907	1,533.0518	1,672.2136	1,904.8008	816.6661	289.8030	699.9995	200.0901
4	0.9650643210	11,563.4007	1,077.1250	3,432.6380	1,519.4832	1,657.4133	1,887.9419	809.4380	287.2380	693.8040	198.3192
5	0.9565227962	11,461.0561	1,067.5917	3,402.2567	1,506.0346	1,642.7439	1,871.2322	802.2739	284.6958	687.6634	196.5639
6	0.9480568701	11,359.6174	1,058.1427	3,372.1442	1,492.7051	1,628.2044	1,854.6705	795.1732	282.1760	681.5770	194.8242
7	0.9396658737	11,259.0765	1,048.7774	3,342.2983	1,479.4936	1,613.7936	1,838.2553	788.1354	279.6785	675.5446	193.0998
8	0.9313491437	11,159.4254	1,039.4949	3,312.7165	1,466.3990	1,599.5104	1,821.9854	781.1598	277.2032	669.5655	191.3908
9	0.9231060229	11,060.6564	1,030.2946	3,283.3965	1,453.4203	1,585.3536	1,805.8595	774.2459	274.7497	663.6394	189.6968
10	0.9149358597	10,962.7615	1,021.1758	3,254.3361	1,440.5564	1,571.3220	1,789.8763	767.3933	272.3180	657.7657	188.0179
11	0.9068380084	10,865.7330	1,012.1376	3,225.5328	1,427.8065	1,557.4147	1,774.0346	760.6013	269.9078	651.9440	186.3538

There is no month-0 strain, and its absence is the product. t = 0 is positive at ₩205.4984 and every row of policy year 1 is positive. A one-year renewable contract with no reserve accumulation and a level expense rate has no acquisition/renewal distinction to create one.

The rows where the product does something

t	pols_if	premiums	claims_ge_in	claims_ge_out	claims_np_in	claims_np_out	claims_np_three	expenses	claim_expenses	commissions	net_cf
11	0.9068380084	10,865.7330	1,012.1376	3,225.5328	1,427.8065	1,557.4147	1,774.0346	760.6013	269.9078	651.9440	186.3538
12	0.8898237107	11,671.5892	1,003.0791	3,196.9486	1,514.5001	1,644.1587	1,891.8205	817.0112	277.5152	700.2954	626.2604
24	0.8269420725	11,255.2428	941.5160	3,001.0022	1,521.4795	1,636.8789	1,909.8972	787.8670	270.3232	675.3146	510.9643
36	0.7807303037	11,657.8250	897.7905	2,861.8800	1,551.7139	1,652.4968	1,957.3942	816.0477	267.6383	699.4695	953.3941
47	0.7546309860	11,268.1113	867.7779	2,766.2092	1,499.8410	1,597.2548	1,891.9597	788.7678	258.6913	676.0867	921.5228
48	0.7447790095	12,234.0846	865.0133	2,757.6339	1,592.1640	1,686.8368	2,022.0773	856.3859	267.7118	734.0451	1,452.2165
59	0.7232591474	11,880.5894	840.0193	2,677.9540	1,546.1596	1,638.0969	1,963.6508	831.6413	259.9764	712.8354	1,410.2557
60	0.7141205641	12,896.5596	1,047.0651	3,151.5278	2,064.9814	2,052.2614	2,600.0030	902.7592	327.4752	773.7936	-23.3071
72	0.6874997399	13,729.9031	1,018.1132	3,064.6451	2,138.8820	2,113.3143	2,709.8504	961.0932	331.3441	823.7942	568.8666
118	0.6087150719	16,301.6322	928.7562	2,796.3637	2,363.0410	2,142.5505	3,033.2096	1,141.1143	337.9176	978.0979	2,580.5814
119	0.6075906434	16,271.5195	927.0406	2,791.1982	2,358.6760	2,138.5928	3,027.6066	1,139.0064	337.2934	976.2912	2,575.8145

What each of those rows is.

• t = 11 — the last month of policy year 1, and the only month of that year in which the renewal decline acts: pols_renewal_decline(11) = 0.0089881183 against pols_lapse(11) = 0.0079263524. The decline is the larger of the two exits at every annual boundary, and by policy year 2 it is nearly twice the lapse.

• t = 12 — the first renewal. net_cf more than triples, from ₩186.35 to ₩626.26, and the reason is worth stating precisely: the 비급여 base premium rises 12.424% while the claim it funds rises only with the 8.1% 비급여 cost trend, and the 급여 base rises 5.04% against a 1.0% claim trend. The premium re-rate outruns the claim trend by construction, because the 4% age loading has no counterpart in a utilisation table that moves in five-year steps.

• t = 24 — the first month of policy year 3, and the first month the 무사고 할인 applies: noclaim_share(3) = 0.729012² = 0.5314584961, so 5.3146% comes off the whole office premium. premiums(24) is therefore ₩11,255.2428 against the ₩11,886.9868 it would have been without the discount, and the year-3 gross premium of ₩13,610.6786 is below the un-discounted ₩14,374.6306 — the discount gives back more than half of the year’s 9.590% re-rate, which becomes +3.766% once it is applied. The two-year lookback is what the launch release’s three-year timeline requires R1, and the model reproduces that leg of it: the discount first appears in year 3. It does not reproduce the release’s other leg — R1 shows years 1 and 2 giving the rider discount, and here they give nothing, because the 요율 상대도 was deferred to 2024-07-01 R3 and reld_start_year = 4.

• t = 36 — policy year 4, where the 요율 상대도 switches on (reld_start_year = 4, the three-year deferral to 2024-07-01 R3). Nothing at all happens in the cash flows: reld_avg(4) = 1.0000000000 exactly, because the discount cap is slack and the scheme is revenue-neutral. The loop’s first live year is the year in which it moves no money, and on a single average cell that is exactly what revenue neutrality means — individual policies are re-rated apart, and the average is not.

• t = 48 — policy year 5, where the discount cap first binds. reld_avg steps to 1.0025494000 and the rider premium rises above its base for the first time.

• t = 59 → t = 60 — the first 재가입 and the utilisation band step at the same anniversary. The 재가입 is a no-op in this model, by assumption; the band step is not. net_cf falls from +₩1,410.2557 to −₩23.3071.

• t = 72 — policy year 7, where the year-6 claim has trended enough to push bucket 8 across ₩3,000,000 into 5단계; reld_avg steps again to 1.0095494000.

• t = 119 — the horizon. pols_renewal_decline(119) = 0.0060646829 and pols_maturity(119) = 0.6004036091 together absorb the whole remaining in-force, and pols_if(120) = 0. The maturity count pays nothing: there is no 만기보험금 on a 순수보장성 contract, and what ends here is the stated horizon, not the cover.

The renewal and experience-rating ledger

result_prem(), one row per policy year — the frame the product’s story is actually in.

y	claims_np_rated_pp	band_1	band_2	band_3	band_4	band_5	reld_surcharge	reld_solved	reld_one	reld_avg	noclaim_share	prem_ge_base	prem_np_base	prem_gross_mth
1	53,531.5106	0.000000	1.000000	0.000000	0.000000	0.000000	1.000000	1.0000000000	1.0000000000	1.0000000000	0.0000000000	4,792.8000	7,189.2000	11,982.0000
2	57,893.3650	0.729012	0.252988	0.008000	0.007000	0.003000	0.301988	0.9574766945	0.9574766945	1.0000000000	0.0000000000	5,034.3571	8,082.3862	13,116.7433
3	62,514.9072	0.729012	0.252988	0.008000	0.007000	0.003000	0.301988	0.9574766945	0.9574766945	1.0000000000	0.5314584961	5,288.0887	9,086.5419	13,610.6786
4	67,434.7704	0.729012	0.252988	0.008000	0.007000	0.003000	0.301988	0.9574766945	0.9574766945	1.0000000000	0.5314584961	5,554.6084	10,215.4538	14,931.9489
5	72,600.0553	0.729012	0.252988	0.000000	0.015000	0.003000	0.309988	0.9465029382	0.9500000000	1.0025494000	0.5314584961	5,834.5607	11,484.6218	16,426.4626
6	95,944.4532	0.729012	0.252988	0.000000	0.015000	0.003000	0.309988	0.9465029382	0.9500000000	1.0025494000	0.5314584961	6,128.6225	12,911.4712	18,059.3589
7	103,291.4952	0.729012	0.252988	0.000000	0.008000	0.010000	0.316988	0.9369009015	0.9500000000	1.0095494000	0.5314584961	6,437.5051	14,515.5924	19,970.7757
8	110,408.5397	0.729012	0.252988	0.000000	0.008000	0.010000	0.316988	0.9369009015	0.9500000000	1.0095494000	0.5314584961	6,761.9553	16,319.0096	22,001.8621
9	118,056.8805	0.729012	0.252988	0.000000	0.008000	0.010000	0.316988	0.9369009015	0.9500000000	1.0095494000	0.5314584961	7,102.7579	18,346.4834	24,262.6066
10	126,324.7368	0.729012	0.252988	0.000000	0.008000	0.010000	0.316988	0.9369009015	0.9500000000	1.0095494000	0.5314584961	7,460.7369	20,625.8505	26,780.3985

Five things to read off it.

1. The band mix at y = 2 is exactly the published commencement distribution — 72.9 / 25.3 / 0.8 / 0.7 / 0.3 R12 — because the shape table is calibrated at the anchor’s year-1 rated claim: C(1) = 53,531.5106 against a tabulated shape_mean() = 53,530.7924. The surcharge pool is 0.301988 and the solved band-1 relativity is 0.9574766945, a 4.2523% discount. That is the specification’s 0.9575 arriving as a result rather than as an input, and it is the single best evidence that the neutrality identity is implemented rather than asserted.

2. y = 1 has no prior year, so every contract sits at 2단계 and the printed reld_solved of 1.0 is the guard value, not a solve. The relativity is not applied in year 1 in any case.

3. The relativity is not applied until y = 4, and when it is applied it moves nothing: reld_avg is 1.0 exactly at y = 4. Revenue neutrality on a single average cell means the loop is invisible in the aggregate until the cap binds.

4. The cap binds from y = 5. The claim level has trended far enough that bucket 7 (tabulated 1,200,000) crosses ₩1,500,000 and moves from 3단계 to 4단계, so reld_surcharge rises from 0.301988 to 0.309988 and the solved discount would be 5.35%; the std 5% cap holds reld_one at 0.95 and reld_avg rises to 1.0025494. From y = 7 bucket 8 crosses ₩3,000,000 into 5단계, the pool reaches 0.316988, and reld_avg reaches 1.0095494. The scheme stops being revenue-neutral at the moment the discount is capped, and after that the loop is a net addition to premium.

5. noclaim_share is 0.5314584961 = 0.729012² from y = 3, two independent claim-free years, giving a 5.3146% discount on the whole office premium.

Hand traces

Four periods, written out term by term, so that a reader with a calculator can reproduce a row and watch the processing order do its work. All arithmetic is on the values printed above.

Trace, t = 0 — the annual claim built from nothing, then divided by twelve.

Step 0: the year's basis.  y = 1, age = 40, band = 40, f_ge = f_np = 1.0
Step 1: the public ceiling.
  C_ge(1)  = ( 0.014140 x 1,184,000 + 1.885433 x 36,100 ) x 1.0
           = ( 16,741.7600 + 68,064.1313 )                  =    84,805.8913
  tau(1)   = min( 1, 3,260,000 / 84,805.8913 )              =     1.0000000000
Step 2 and 3: co-payment, deductible, and the inpatient cap.
  geubyeo inpatient
    cost     = 0.014140 x 1,184,000 x 1.0 x 1.0             =    16,741.7600
    retained = 0.20 x 16,741.7600 = 3,348.3520 < 2,000,000  -> top_up = 0
    paid     = 0.80 x 16,741.7600                           =    13,393.4080
  geubyeo outpatient, per visit, over the distribution
    clinic tier, floor 10,000:
      8,000  -> ded max(10,000, 1,600)  = 10,000 -> pay      0.00 x 0.30
      18,000 -> ded max(10,000, 3,600)  = 10,000 -> pay  8,000.00 x 0.30
      40,000 -> ded max(10,000, 8,000)  = 10,000 -> pay 30,000.00 x 0.25
      90,000 -> ded max(10,000, 18,000) = 18,000 -> pay 72,000.00 x 0.12
      250,000-> ded max(10,000, 50,000) = 50,000 -> pay min(200,000, 200,000) x 0.03
      = 0 + 2,400 + 7,500 + 8,640 + 6,000                   =    24,540.0000
    hospital tier, floor 20,000: 0 + 0 + 5,000 + 8,400 + 6,000
                                                            =    19,400.0000
    blend   = 0.63 x 24,540 + 0.37 x 19,400                 =    22,638.2000
    paid    = 1.885433 x 22,638.2000                        =    42,682.8093
  bigeubyeo inpatient
    base    = 1,716,000 x 1.0 x 0.70                        = 1,201,200.0000
    room    = 0.55 x min(0, 750,000) + 0.30 x min(150,000, 750,000)
              + 0.15 x min(600,000, 750,000)                =   135,000.0000
    paid    = 0.014140 x ( 1,201,200 + 135,000 )            =    18,893.8680
  bigeubyeo outpatient, per visit
    45,000 -> ded max(30,000, 13,500) = 30,000 -> pay  15,000 x 0.35
    90,000 -> ded max(30,000, 27,000) = 30,000 -> pay  60,000 x 0.30
    180,000-> ded max(30,000, 54,000) = 54,000 -> pay 126,000 x 0.22
    400,000-> ded max(30,000, 120,000)= 120,000-> pay min(280,000, 200,000) x 0.10
    900,000-> ded max(30,000, 270,000)= 270,000-> pay min(630,000, 200,000) x 0.03
    = 5,250 + 18,000 + 27,720 + 20,000 + 6,000              =    76,970.0000
    visits  = min( 0.236694, 100 )                          =     0.2366940
    out     = 0.236694 x 76,970                             =    18,218.3372
Step 4: the three named classes, and the injection carve-out.
  per act: physio 97,020   inject 121,200   mri 467,250
  physio acts  = min(0.092047, 50) = 0.092047 <= 10, so no gate
    claim      = min( 0.092047 x 97,020, 3,500,000 )        =     8,930.3999
  inject acts  = min(0.078898, 50) x (1 - 0.25) = 0.0591735
    claim      = min( 0.0591735 x 121,200, 2,500,000 )      =     7,171.8282
    carve      = 0.078898 x 0.25 x 121,200                  =     2,390.6094
  mri          = min( 0.015780 x 467,250, 3,000,000 )       =     7,373.2050
  NP_OUT       = 18,218.3372 + 2,390.6094                   =    20,608.9466
  NP_THREE     = 8,930.3999 + 7,171.8282 + 7,373.2050       =    23,475.4331
Step 5: the annual aggregates.  raw_ge = 56,076.2173, raw_np = 39,502.8146.
  The test is sigma x raw <= 50,000,000 on each bojang jongmok, i.e.
  raw <= 50,000,000 / 0.15 = 333,333,333 and 50,000,000 / 0.85
  = 58,823,529; both raws are three orders below the tighter of
  the two, so g_ge(1) = g_np(1) = 1.0000000000
claims_ann_pp(1) = 13,393.4080 + 42,682.8093 + 18,893.8680
                 + 20,608.9466 + 23,475.4331                =   119,054.4651
loss_incurred_pp(1)                                         =   186,006.8254
  -> the claim is 64.005% of the covered loss; the rest is
     the 20/30% retention and the flat deductibles.

Month 0 itself, at l(0) = 1.0000000000:
  premiums       = 11,982.0000 x 1.0000000000               =    11,982.0000
  claims_ge_in   = 13,393.4080 / 12 x 1.0                   =     1,116.1173
  claims_ge_out  = 42,682.8093 / 12 x 1.0                   =     3,556.9008
  claims_np_in   = 18,893.8680 / 12 x 1.0                   =     1,574.4890
  claims_np_out  = 20,608.9466 / 12 x 1.0                   =     1,717.4122
  claims_np_three= 23,475.4331 / 12 x 1.0                   =     1,956.2861
  claims         = 119,054.4651 / 12                        =     9,921.2054
  expenses       = 0.07 x 11,982.0000                       =       838.7400
  claim_expenses = 0.03 x 9,921.2054                        =       297.6362
  commissions    = 0.06 x 11,982.0000                       =       718.9200
  net_cf         = 11,982.0000 - 9,921.2054 - 838.7400
                   - 297.6362 - 718.9200                    =       205.4984
  cross-check    = 0.87 x 11,982.0000 - 1.03 x 9,921.2054   =       205.4984
Decrements at the end of month 0 ( (0+1) mod 12 != 0, so no renewal decline ):
  pols_death  = 1.0000000000 x 0.0001100825                 = 0.0001100825
  BEF_LAPSE   = 1.0000000000 x (1 - 0.0001100825)           = 0.9998899175
  pols_lapse  = 0.9998899175 x 0.0087416110                 = 0.0087406487
  l(1)        = 0.9998899175 x (1 - 0.0087416110)           = 0.9911492689

Trace, t = 1 — the scaling row, and why every other month of the year is one.

l(1) = 0.9911492689.  y = 1 still, age 40 still, so every per-policy quantity
of the trace above is unchanged and month 1 is month 0 scaled:
  premiums        = 11,982.0000    x 0.9911492689           =    11,875.9505
  claims_ge_in    =  1,116.1173333 x 0.9911492689           =     1,106.2389
  claims_ge_out   =  3,556.9007784 x 0.9911492689           =     3,525.4196
  claims_np_in    =  1,574.4890000 x 0.9911492689           =     1,560.5536
  claims_np_out   =  1,717.4122150 x 0.9911492689           =     1,702.2119
  claims_np_three =  1,956.2860950 x 0.9911492689           =     1,938.9715
  expenses        =    838.7400000 x 0.9911492689           =       831.3165
  claim_expenses  =    297.6361627 x 0.9911492689           =       295.0019
  commissions     =    718.9200000 x 0.9911492689           =       712.5570
  net_cf          =    205.4984156 x 0.9911492689           =       203.6796
  l(2)            = 0.9911492689 x (1 - 0.0001100825)
                                   x (1 - 0.0087416110)     = 0.9823768732

The whole of policy year 1 is one set of rates and one linear scaling. That is a property of this product, not a shortcut: every contractual mechanism resets annually, so the month carries no information the year does not. The consequence for a reader is that a monthly grid here buys timing and nothing else — and, on an undiscounted projection, timing buys nothing at all. The grid is monthly because the premium mode is monthly and because the decrements are, not because the benefit is.

Trace, t = 11 → t = 12 — the renewal, decrement first and then the re-rate.

Decrements at the end of month 11.  (11+1) mod 12 = 0, so the renewal
decline acts, after mortality, lapse and suspension:
  l(11)         = 0.9068380084
  pols_death    = 0.9068380084 x 0.0001100825               = 0.0000998270
  BEF_LAPSE     = 0.9068380084 - 0.0000998270               = 0.9067381814
  pols_lapse    = 0.9067381814 x 0.0087416110               = 0.0079263524
  BEF_SUSPEND   = 0.9067381814 - 0.0079263524               = 0.8988118290
  pols_suspend  = 0.8988118290 x 0                          = 0.0000000000
  BEF_RENEWAL   = 0.8988118290
  pols_renewal_decline = 0.8988118290 x 0.01                = 0.0089881183
  l(12)         = 0.8988118290 x (1 - 0.01)                 = 0.8898237107
  roll-forward  = 0.9068380084 - 0.8898237107 - 0.0000998270
                  - 0.0079263524 - 0 - 0.0089881183 - 0     = 0.0000000000

The re-rate.  y = 2, age 41.  b_ge = clip(0.010, +-0.25) = 0.010;
b_np = clip(0.081, +-0.25) = 0.081.  The corridor applies to the
AGE-ADJUSTED prior premium:
  G_ge(2) = 4,792.80 x 1.04 x 1.010 = 4,792.80 x 1.05040    =     5,034.3571
  G_np(2) = 7,189.20 x 1.04 x 1.081 = 7,189.20 x 1.12424    =     8,082.3862
  R(2)    = 1.0  (reld_start_year = 4, so the loop is not yet live)
  nc(2)   = 0    (y < 3)
  G(2)    = ( 5,034.3571 + 8,082.3862 x 1.0 ) x (1 - 0)     =    13,116.7433
  step    = 13,116.7433 / 11,982.0000                       = +9.4704%
            of which the geubyeo unit +5.040% and the
            bigeubyeo unit +12.424%
Month 12, at l(12) = 0.8898237107:
  premiums        = 13,116.7433 x 0.8898237107              =    11,671.5892
  claims_ge_in    = 13,527.3421 / 12 x 0.8898237107         =     1,003.0791
  claims_ge_out   = 43,113.4649 / 12 x 0.8898237107         =     3,196.9486
  claims_np_in    = 20,424.2713 / 12 x 0.8898237107         =     1,514.5001
  claims_np_out   = 22,172.8241 / 12 x 0.8898237107         =     1,644.1587
  claims_np_three = 25,512.7458 / 12 x 0.8898237107         =     1,891.8205
  claims          = 124,750.6482 / 12 x 0.8898237107        =     9,250.5071
  expenses        = 0.07 x 11,671.5892                      =       817.0112
  claim_expenses  = 0.03 x 9,250.5071                       =       277.5152
  commissions     = 0.06 x 11,671.5892                      =       700.2954
  net_cf          = 0.87 x 11,671.5892 - 1.03 x 9,250.5071  =       626.2604

The premium falls month by month inside a policy year and rises at the boundary, and both movements are the same fact seen twice: premiums(t) = G(y) × l(t), so inside a year only l moves and it only falls, while at the boundary the +9.4704% re-rate outweighs twelve months of decrement. The net_cf triples because the claim, spread evenly through the year, rises only with the 8.1% and 1.0% cost trends while the premium rises with those trends and the 4% age loading.

Trace, t = 59 → t = 60 — the 재가입 that does nothing and the band step that does everything.

y = 6, age 45, and util_band(6) = 45 for the first time.  The five-year
bojang naeyong byeongyeong jugi also falls here, and is a NO-OP by
assumption: nothing in the model changes at re-entry.
New frequencies, all from the (M, 45) row:
  adm 0.017674 (x1.2499), visits_ge 2.224811 (x1.18),
  visits_np 0.279298 (x1.18), physio 0.112298 (x1.22),
  inject 0.096255 (x1.22), mri 0.020198 (x1.28), los 8.25 (x1.10)
Trends at y = 6:  f_ge = 1.010^5 = 1.0510100501,
                  f_np = 1.081^5 = 1.4761431304
  C_ge(6) = ( 0.017674 x 1,184,000 + 2.224811 x 36,100 ) x 1.0510100501
          = ( 20,926.0160 + 80,315.6771 ) x 1.0510100501    =   106,406.0369
  tau(6)  = min( 1, 3,260,000 / 106,406.0369 )              =     1.0000000000
  GE_IN   = 0.017674 x 1,184,000 x 1.0510100501 x 0.80      =    17,594.7625
  GE_OUT  = 2.224811 x [ 0.63 x e(clinic) + 0.37 x e(hosp) ]=    52,957.9121
  NP_IN   = 0.017674 x [ 1,716,000 x 1.4761431304 x 0.70
                         + room(8.25 days) ]                =    34,699.7101
  NP_OUT  = 0.279298 x e(np_out) + carve                    =    34,485.9651
  NP_THREE= 16,430.9164 + 13,328.1121 + 13,931.1237         =    43,690.1521
  claims_ann_pp(6)                                          =   183,428.5019
Premium: G_ge(6) = 6,128.6225, G_np(6) = 12,911.4712,
         R(6) = 1.0025494000, nc(6) = 0.5314584961
  G(6) = ( 6,128.6225 + 12,911.4712 x 1.0025494 )
         x ( 1 - 0.10 x 0.5314584961 )                      =    18,059.3589
Month 60, at l(60) = 0.7141205641:
  premiums = 18,059.3589 x 0.7141205641                     =    12,896.5596
  claims   = 183,428.5019 / 12 x 0.7141205641               =    10,915.8388
  net_cf   = 0.87 x 12,896.5596 - 1.03 x 10,915.8388        =       -23.3071

The step, decomposed:  claims x 1.2758, premium x 1.0994, so the
loss ratio jumps from 0.7294 to 0.8464, through the model's own
break-even of 0.8447 -- and policy year 6 is the only negative year
in the projection.

Why the negative year is a property of a banded table and not a defect. Holding the frequencies at the (M, 40) row and letting only the trend run would give a year-6 claim of ₩150,937.05 against the model’s ₩183,428.50 — the band step alone is worth +21.53%, or 1.0398 a year compounded over the five years of age it represents. The 표준약관’s stylised age loading is 1.04 a year, and 1.04^5 = 1.216653 against the table’s 1.215265: the utilisation table’s five-year step and the wording’s 4% annual loading agree to within 0.12%. They simply do not arrive at the same time. The premium takes the age effect smoothly at every renewal; the claim takes it in one jump every five years. So the loss ratio saw-tooths, and the trough-to-peak swing is the whole of the model’s margin.

Undiscounted totals over the 120 months

Per policy issued. pols_if sums to months of exposure.

Item	Value
pols_if (sum)	88.998122 policy-months = 7.416510 policy-years
premiums	1,558,165.4328
claims_ge_in	115,320.6688
claims_ge_out	357,128.9114
claims_np_in	222,875.2985
claims_np_out	223,623.9771
claims_np_three	282,146.3147
claims, all five limbs	1,201,095.1706
expenses	109,071.5803
claim_expenses	36,032.8551
commissions	93,489.9260
net_cf	118,475.9008
loss ratio over the projection	0.770839
margin, net_cf ÷ premiums	0.076036

Policy-year totals, which is the clock everything runs on:

policy year	attained age	pols_if months	premiums	claims, all five	expenses	claim_expenses	commissions	net_cf	loss ratio
1	40	11.432747	136,987.1764	113,426.6331	9,589.1024	3,402.7990	8,219.2306	2,349.4114	0.828009
2	41	10.374553	136,080.3438	107,852.6803	9,525.6241	3,235.5804	8,164.8206	7,301.6384	0.792566
3	42	9.710708	132,169.3262	105,812.7236	9,251.8528	3,174.3817	7,930.1596	6,000.2085	0.800585
4	43	9.211361	137,543.5718	105,256.6906	9,628.0500	3,157.7007	8,252.6143	11,248.5162	0.765261
5	44	8.807655	144,678.6216	105,530.7628	10,127.5035	3,165.9229	8,680.7173	17,173.7150	0.729415
6	45	8.460681	152,794.4700	129,327.4993	10,695.6129	3,879.8250	9,167.6682	−276.1354	0.846415
7	46	8.152615	162,814.0368	130,973.1958	11,396.9826	3,929.1959	9,768.8422	6,745.8204	0.804434
8	47	7.871220	173,181.5075	132,415.0893	12,122.7055	3,972.4527	10,390.8905	14,280.3696	0.764603
9	48	7.610823	184,658.3987	134,200.7651	12,926.0879	4,026.0230	11,079.5039	22,426.0188	0.726751
10	49	7.365760	197,257.9800	136,299.1308	13,808.0586	4,088.9739	11,835.4788	31,226.3379	0.690969

The annual per-policy claim quantities behind those totals, which is where the contractual machinery is visible:

y	age	band	oop_incurred_ge	oop_trunc	claims_ge_in_pp	claims_ge_out_pp	claims_np_in_pp	claims_np_out_pp	claims_np_three_pp	claims_ann_pp	loss_incurred_pp	claims_np_rated_pp
1	40	40	84,805.8913	1.0000	13,393.4080	42,682.8093	18,893.8680	20,608.9466	23,475.4331	119,054.4651	186,006.8254	53,531.5106
2	41	40	85,653.9502	1.0000	13,527.3421	43,113.4649	20,424.2713	22,172.8241	25,512.7458	124,750.6482	195,052.1600	57,893.3650
3	42	40	86,510.4897	1.0000	13,662.6155	43,548.4269	22,078.6373	23,753.2315	27,715.0809	130,757.9921	204,769.9545	62,514.9072
4	43	40	87,375.5946	1.0000	13,799.2417	43,987.7386	23,850.1902	25,399.2461	30,085.5877	137,122.0043	215,214.0760	67,434.7704
5	44	40	88,249.3506	1.0000	13,937.2341	44,431.4435	25,653.2049	27,178.5880	32,580.0369	143,780.5073	226,442.7489	72,600.0553
6	45	45	106,406.0369	1.0000	17,594.7625	52,957.9121	34,699.7101	34,485.9651	43,690.1521	183,428.5019	288,743.9336	95,944.4532
7	46	45	107,470.0973	1.0000	17,770.7101	53,492.0076	37,333.2268	36,886.9549	47,299.2243	192,782.1238	304,577.3636	103,291.4952
8	47	45	108,544.7983	1.0000	17,948.4172	54,031.4440	40,180.0584	38,542.0111	51,170.3302	201,872.2610	321,617.7532	110,408.5397
9	48	45	109,630.2463	1.0000	18,127.9014	54,576.2748	43,257.4834	40,317.8373	55,315.1269	211,594.6238	339,962.1105	118,056.8805
10	49	45	110,726.5487	1.0000	18,309.1804	55,126.5540	46,584.1798	42,237.5054	59,795.6522	222,053.0718	359,715.2940	126,324.7368

Reading the shape of the result

The stream is positive in every policy year but one, and the one exception is policy year 6, at −₩276.14. That is the whole shape, and it decomposes cleanly because the ledger collapses to net_cf = 0.87 × premiums − 1.03 × claims: the sign of any period is decided by one number, the loss ratio, against the model’s own break-even of 0.844660. Year 1 runs at 0.828009 — which is not an accident but the calibration, reproducing the published 4세대 2022 상반기 combined 경과손해율 of 82.8% on the published ₩11,982 premium anchor R12 R1 — so the product opens with a margin of about 1.7% of premium and a claim that is already 98% of the way to break-even. On a real 4세대 book that margin was not there: the generation ran 91.5% in 2022, 113.8% in 2023, 111.9% in 2024 and 115.1% in 2025 R7 R8, and product-spec.md explains why a newly launched Korean generation is under-priced by regulatory construction — the five-year grace on rate-adequacy verification of 감독규정 제7-63조제2항제6호가목 meant 4세대 first re-rated in 2025, and it was priced off 「’16년도 2세대 요율」 to begin with R12 REG-R17. The model reproduces the published 2022 loss ratio and then lets the contractual re-rating machinery run; the real book did not get to re-rate for four years. The gap between this projection’s +₩118,476 and the line’s actual −₩1.87조 underwriting result in 2025 R7 is that four-year freeze, not a difference of view about the mechanics.

Inside that, the loss ratio saw-tooths downward: 0.828, 0.793, 0.801, 0.765, 0.729, then a jump to 0.846 at the band step, then 0.804, 0.765, 0.727, 0.691. Two forces make the teeth. The premium takes its 4% age loading smoothly at every renewal, nine times over the projection, compounding to 1.04⁹ = 1.4233; the claim takes its age effect in one 21.53% step, at attained age 45, because the utilisation table is banded in fives and the next step falls at age 50, one year beyond the horizon. So the projection catches one of the two steps the age loading is paying for, and the loss ratio drifts down by about a sixth over ten years. That drift is a horizon artefact and would reverse at policy year 11, and saying so is more useful than smoothing the table would be: a five-year banded basis and an annual age loading do not compose smoothly, and a ten-year run from an issue age of 40 lands asymmetrically on the boundary.

The composition of the claim is not what the market narrative suggests. 급여 통원 is the single largest limb at 29.73% of the ten-year claim, and the whole 급여 half is 39.33% against 60.67% 비급여 — close to, and 3.6 points above, the 57.1% 비급여 share the supervisor reports for 2025 R7, and far above 비급여’s 15.8% share of national medical spend R9. The 3대비급여 classes alone are 23.49% of the claim on a cell that is not a heavy user of them. And the 급여 unit runs at a loss ratio of 0.975 in year 1 against the 비급여 unit’s 0.730 — the main contract is the worse half, throughout, which is exactly what the published 4세대 statistics show (급여 97.5% / 154.6%, 비급여 73.0% / 114.2% between 2022 H1 and 2024 H1 R12) and exactly the opposite of what a reader primed by the 비급여 할인·할증 publicity would expect. A model that treats the 급여 unit as the stable half will mis-project the renewal path.

Finally, the loop does very little on an average cell, and that is the correct answer. Over ten years the experience relativity moves the average rider premium by at most 0.95% (reld_avg reaching 1.0095494), and for the first four years by nothing at all. That is what revenue neutrality means: the surcharge funds the discount, so the average is untouched until the std 5% cap on the discount breaks the neutrality. The scheme’s whole effect is cross-sectional — a band-5 policyholder pays 0.40 + 0.60 × 4.00 = 2.80× the base total premium while a band-1 policyholder pays 0.40 + 0.60 × 0.9575 = 0.9745× — and a single average cell cannot show it. What the average cell can show, and does, is the migration: with fixed money thresholds and a trending claim, contracts cross into the surcharge bands year after year. The 3단계 buckets empty entirely by policy year 5, and the 5단계 contribution to the surcharge pool rises from 0.012 at commencement to 0.040 by policy year 7 — a factor of 3.33 — while the pool above the 2단계 base goes from 0.049 to 0.064. That migration is the part of the design that compounds, and it is the reason the discount cap binds at all.

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Valuation and reserve pointers

This model projects gross, undiscounted liability cash flows. Every valuation layer below consumes them and is cited, never reproduced. Korea is the only market in this repository running three of them at once and all three live.

• 책임준비금. 보험업법 제120조제1항 requires a 책임준비금 and a 비상위험준비금 at each 결산기, carrying no method and no rate itself REG-R3. 시행령 제63조제1항, amended 2022-12-27, restates the reserve in IFRS 17 vocabulary as 보험계약부채 = 발생사고요소 + 잔여보장요소, both on a 현행추정치 basis, and confines 비상위험준비금 to non-life business REG-R8. On a one-year indemnity contract the weighting inverts relative to every other krlib product: the 잔여보장요소 is at most one policy year’s unearned premium, and the 발생사고요소 — claims incurred and not yet settled — is the material item. That is the reserving consequence of a monthly-mode contract with a 3 영업일 / 30 영업일 settlement timetable [S1 제8조] and it is not a consequence this projection computes.

• 해약환급금준비금 has nothing to bite on. 감독규정 제6-11조의6 creates the Korea-specific overlay because IFRS 17 measurement can fall below the contractual surrender value REG-R11. There is no surrender value here at all [S3], so the overlay is identically nil — the only product in krlib of which that is true. The 표준해약공제액 cap of [별표 14] likewise does not engage REG-R20, and neither do the 해약환급금 articles 제7-66조 through 제7-70조 except for the 미경과보험료 limb of 제7-66조제5항 REG-R19 REG-R17.

• K-ICS. In force since 2023-01-01. 시행령 제65조제2항제1호 states the requirement in one line — 「지급여력비율은 100분의 100 이상을 유지할 것」 REG-R8 — and 감독규정 제7-2조제2항 decomposes the 생명·장기손해보험위험액 into seven sub-risks, of which three bear directly on this contract: 장해·질병위험액 (a shock to morbidity), 해지위험액 (「보험계약자의 옵션행사율 변화 또는 보험계약 대량해지」) and 대재해위험액 for epidemics and mass accidents, measured by 위험계수방식 rather than by shock REG-R13. A one-year renewable indemnity contract is the archetype of a product whose charge is dominated by the morbidity shock and by the lapse-option risk — the renewal decline is literally an 옵션행사율 — and whose interest-rate exposure is negligible. What this model owes that regime is the capability it demands: a frequency and severity basis parameterized so that a shock can be applied per grouping, and a decrement structure in which the renewal option is a separate rate. It computes no 요구자본.

• IFRS 17, and the boundary. K-IFRS 제1117호 has been mandatory for Korean insurers since 2023-01-01 — not voluntary as in Japan REG-R60. The boundary question this contract raises is genuine and this document asserts no answer: a one-year term, an unrestricted right to re-rate, a supervisor-set ±25% cap on that re-rating, a five-year re-entry into a wording the insurer does not control, and an obligation not to refuse re-entry on health grounds [S1 제23조] [S1 제30조] REG-R17. Pulling the other way is the wording’s own 「종전 계약의 보험기간을 연장하는 것으로 보아」 at 제3조제6항 [S1], which makes renewal and re-entry continuations for benefit purposes. Nothing retrieved states an industry or supervisory position on where the boundary falls for that combination, and the general boundary test was read only in secondary summary form unverified. Medical_KR_S projects to a stated horizon on stated terms and computes no CSM; a user who takes the boundary at one year should read only t = 0 … 11, and a user who takes it at the 재가입 should read t = 0 … 59. Both readings are available in the same frame, which is the point of publishing the whole of it.

• Rate adequacy is a supervisory obligation, and it is what the renewal machinery serves. 감독규정 제7-63조제2항제6호가목 requires 「경험통계 등을 기초로 순보험요율의 적정성을 매년 검증할 것」, with up to five years’ grace for genuinely new cover R12 REG-R17. The 보험연구원’s principal recommendation is to shorten the grace to three years R12. And 제7-45조제7항 requires the 보험가격지수 — 보험료총액 ÷ (참조순보험료 총액 + 보험회사 평균사업비총액) — to be explained to a 실손 policyholder at every renewal, not only at sale REG-R22. For this product that index has no denominator: there is no 실손 참조순보험요율 R20.

• Not applicable. 계약자배당 and the surplus-distribution machinery REG-R12 do not attach — the contract is 순수보장성 with no 계약자적립액. 비상위험준비금 is confined to non-life business and is asset- and catastrophe-driven rather than a liability projection REG-R8. 특별계정 does not arise REG-R6 REG-R15.

• Policyholder tax, not modelled. The premium qualifies for the 보장성보험료 세액공제 of 소득세법 제59조의4제1항 — a credit of 12% of premiums paid, capped at ₩1,000,000 of premium a year REG-R57. On the anchor cell that is ₩11,982 × 12 = ₩143,784 of first-year premium, well inside the cap, for a credit of about ₩17,254 before the local surtax. It is a credit and not a deduction, which changes the after-tax comparison against every other market in this repository. Benefits are not projected net of policyholder tax.

• What this model does not compute, listed so that nothing downstream assumes it does. No 책임준비금, no CSM, no risk adjustment, no fulfilment cash flow, no K-ICS requirement, no 해약환급금준비금, no 비상위험준비금, no discounting and no policyholder tax.

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Key sensitivities and model risks

In rough order of leverage on a 실손 block.

1. The whole claim basis is std, and it has no public counterpart to be checked against. Frequency, severity, the annual-claim shape and the zero-claim mass are four independent constructions on aggregate supervisory experience R7 R8 R12, not an insurer’s 위험률 — which is unpublished by regulation REG-R2 — and not a 참조순보험요율, because none exists for this product R20. The level is pinned by one solve against one published pair of loss ratios in one half-year R12; everything else about the basis is shape. A user with company data should replace all four tables before drawing any conclusion, and the provenance column on every row exists for exactly that.

2. The severity distribution, not its mean. The deductible is max(flat floor, percentage), so the payment is kinked and the shape decides the claim. Substituting each stream’s mean for its distribution changes the 비급여 통원 payment by +35.83% (₩104,545 against ₩76,970) and the 급여 통원 hospital tier by −17.01%, while leaving MRI unchanged, because every MRI point sits above its crossing. The dispersion being standardized over is real and published: 도수치료 quoted between ₩5,000 and ₩600,000 across Seoul hospitals R2.

3. The 급여/비급여 boundary moves inside any realistic horizon, and the model holds it fixed. 요양급여 covers everything except what the 보건복지부장관 designates 비급여대상, so 비급여 is a residual defined by exclusion from a list that changes REG-R53. 5세대’s 관리급여 category migrates over-used 비급여 items into the covered system at a 95% co-payment R6: if 도수치료 becomes 관리급여 it leaves the rider entirely and enters the main contract, changing which unit is re-rated, which claim counts for the 요율 상대도, and which limit applies. A model that assumes a static partition will be wrong within the projection horizon.

4. The two cost trends carry the whole re-rating, and they are one year’s national growth rates. med_trend_ge = 1.0% and med_trend_np = 8.1% are 2024 figures R9 REG-R41. The whole premium path, the loop’s band migration and the corridor’s bite are functions of them. At trend_mult = 4.5 (model point 10) the 비급여 re-rate would be 36.45% and the corridor clips it to 25%.

5. The corridor is a weaker constraint than it looks. The ±25% corridor and the 4% age loading compose, so the wording admits a re-rate of 1.25 × 1.04 = 1.30 a year on a single 위험구분단위; the corridor does not bind economically below about a 30% claim trend. On model point 10, whose 비급여 re-rate is clipped from 36.45% to 25% in every one of nine renewals, the ten-year loss ratio still rises only from 0.533 to 0.591. That is a model finding worth printing, and it cuts against the intuition that a 25% cap is the binding constraint on Korean 실손 pricing.

6. The band-1 discount is a solved quantity and it is sensitive to a distribution nobody publishes twice the same way. On the 손보 commencement mix 72.9 / 25.3 / 0.8 / 0.7 / 0.3 R12 the identity gives a 4.25% discount; on the FSC’s 62.1 / 36.6 / 1.3 R3 it gives 2.1%. The published statements bracket both — 「5% 내외」 R1, −5% 잠정 R3, 95% in the wording’s illustration [S1] — and the std 5% cap is the only thing stopping the solve running away once the claim level trends. The cap’s level is the single assumption with the largest effect on the loop’s aggregate behaviour, and it has two published anchors and no observed range.

7. The zero-claim mass is held constant and it would not be. claim_shape_table.csv trends its amounts and not its frequency, so 72.9% of contracts have no rated claim in every projected year. In reality the frequency of claiming rises with age, the 1단계 share falls, w₁ shrinks, and the solved discount deepens for the survivors while the surcharge pool grows. Both effects push reld_avg up faster than this model shows.

8. Successive years’ claiming is assumed independent, and it is not. The 무사고 할인 share is w₁(y−1) × w₁(y) = 0.729012² = 0.5315 std. Real claiming persists, so the true share of two-year claim-free contracts is higher than the independent product, and this model therefore understates the discount and overstates the premium. Nothing published gives the persistence of claiming.

9. Mortality runs the wrong way here. Death releases the liability on this contract, so an over-statement of mortality is anti-conservative — the reverse of every protection product in krlib. Over the ten projected years the anchor cell loses 0.011647 of a policy to death against 0.315540 to lapse and 0.072409 to the renewal decline, so the exposure is small here; on a projection to the maximum cover age of 100 it would not be.

10. Lapse and the renewal decline are one published number split three ways. The 3.3% blended in-force decay of the 1–3세대 block R7 is the only 실손-specific persistency figure there is, and it contains lapse, death, conversion and renewal decline together. The split into a 10% → 2% lapse curve and a 1% renewal decline is std, and the first-year rate rests on an unverified news figure. On a product with no surrender value, no policy loan and an annual re-rate, persistency is a first-order driver.

11. The behavioural response is unmodelled and the supervisor says it is the point. R2’s own example has a policyholder cutting claims by 93% under a surcharge. A model that projects the premium’s response to claims without the claims’ response to premium overstates the surcharge revenue and understates the discount take-up in the same breath.

12. Concentration. 65% of insureds claim nothing in a year and the top decile takes about 74% of all claims R4 R5 R6. A single cell carrying the population mean frequency is not a policyholder anybody would recognise, and it is the reason model point 8 exists at util_mult = 10 — the only shipped point on which the 본인부담상한제 truncation binds, taking it from 0.8018 in policy year 1 to 0.6024 by policy year 10 and driving reld_avg to 1.3290.

13. The 재가입 is modelled as a no-op and it is not one. At t = 60 the contract in reality re-enters the generation then on sale, at that generation’s partition, co-payments and limits and at a premium the insurer sets for it. The 5세대 deltas in product-spec.md change the rider into two riders, the 비중증 co-payment to 50%, the 비중증 annual limit to ₩10,000,000 and the relativity’s scope to 특약2 only [S2] R5 R6. Anything this projection says about policy years 6–10 is a statement about 4세대 terms that will not be in force.

14. Two clocks that are never reconciled. The 본인부담상한제 runs on the calendar year R10; every contractual limit runs on the policy year [S1 제5조제2항]; and the insurer’s own experience statistics run on the calendar year R7 R8. This model runs everything on the policy year and says so.

Known modeling pitfalls

Each of these is a mistake a competent modeller would actually make on this product, and each is checkable against the shipped model.

• Do not multiply a rate by the 보험가입금액. There is no sum assured here. The ₩50,000,000 is an annual cap, and it may appear in a formula only inside a min. Any expression in which annual_limit() is a multiplier has the dimensions of money and the meaning of nothing. This is the single commonest error made by an actuary arriving from a fixed-benefit 제3보험 product, and check_indemnity() is the constraint that catches it: claims_ann_pp(y) ≤ loss_incurred_pp(y), with year 1 at 119,054.4651 ≤ 186,006.8254, a ratio of 0.6401.

• Apply the deductible to the distribution, not to the mean. For the 비급여 통원 stream E[max(0, X − max(30,000, 0.30X))] = 76,970 while max(0, μ − max(30,000, 0.30μ)) = 104,545 — +35.83%. The trap is that the error can hide: on the 급여 통원 limb the clinic tier is +6.36% and the hospital tier −17.01%, and the blend at clinic_share = 0.63 comes out only −1.05% wrong. A model that checks the blend and not the tiers will pass its own test and misprice both providers.

• The 본인부담상한제 is an exclusion from covered loss, not a cap on the benefit, and it goes first. oop_trunc(y) multiplies the incurred cost inside paid_out_per_visit, so it changes where the deductible bites; applying it to the finished claim instead is linear on the inpatient limb and wrong on the outpatient limb, where the deductible is kinked. check_oop_ceiling() asserts the statement about the loss — oop_incurred_ge(y) × oop_trunc(y) ≤ oop_ceiling() — and not a statement about the benefit. On the anchor oop_trunc ≡ 1.0 and the error is invisible; on model point 8 it is not, which is why that model point exists.

• The ₩2,000,000 inpatient co-payment cap sits on the retention that survives the ceiling. Both reduce the insured’s retention on heavy 급여 use, so applying them in parallel, or the cap first, double-counts the relief. claims_ge_in_pp computes cost = adm × μ × trend × trunc and then top_up = max(0, cost × r_ge − 2,000,000) in that order.

• The corridor applies to the age-adjusted prior premium, and the wording’s own label misleads. 「기초율 증가분 = 전년도 기준보험료 × 25%」 reads as additive, but 3,640 is 25% of 14,000 × 1.04 [S1 제30조]. prem_np_base(10) = 20,625.8505 on the correct recursion 7,189.20 × (1.04 × 1.081)⁹ and 20,096.9929 on the additive misreading — 2.564% low, and compounding. check_renewal_corridor() measures the move against the age-adjusted prior premium and per 위험구분단위, so it catches the loading applied on the wrong side of the clip.

• The experience relativity touches the rider and nothing else. Applying reld_avg(y) to the whole office premium gives a year-5 gross of ₩16,440.5468 instead of ₩16,426.4626. 「비급여 특약 보험료만 할증되며 보험료 전체가 할증되는 것은 아닙니다」 R2.

• The band-1 relativity is solved, not 0.95. Hard-coding the illustration’s 95% [S1] from policy year 2 gives reld_avg = 0.729012 × 0.95 + 0.301988 = 0.9945494 — a 0.55% leak out of a scheme the wording requires be self-financing, growing as the band mix moves. check_relativity_neutral() asserts Σ_b w_b r_b = 1 exactly while the discount cap is slack, and asserts only that the scheme never funds a discount it has not collected once the cap binds.

• The 무사고 할인 has a two-year lookback and the relativity has one. noclaim_share(3) = band_share(2, 1) × band_share(3, 1) = 0.729012² = 0.5314584961, not 0.729012. A one-year lookback gives a year-3 office premium of ₩13,326.7028 against the correct ₩13,610.6786 — 2.09% low — and hands the 10% discount to policyholders who have earned one clean year rather than two. The two reliefs also apply to different bases: the relativity to the rider, the 무사고 할인 to the whole premium.

• There is no no-claims ladder. 「보험금 지급(사고) 이력이 1년마다 초기화됩니다」 R2. band_share(y, b) reads claims_np_rated_pp(y − 1) and nothing earlier. A model that accumulates band state across years invents a persistence the wording explicitly removes, and turns a memoryless one-year lookback into a bonus-malus chain.

• The injection carve-out must be counted once. 25% of the injection acts leave the ₩2,500,000 sub-limit for the main ₩50,000,000 limit [S1 특별약관 제3조(3)제2항], so acts_inject_eff(1) = 0.75 × 0.078898 = 0.0591735 and the carved payment ₩2,390.6094 is added in claims_np_out_pp, not in claims_np_three_pp. Double-counting it inflates the year-1 claim by 2.0%; forgetting the removal from acts_inject_eff deflates it by the same amount and puts the money under the wrong limit.

• Read the utilisation table at the attained age, not the issue age. util_band(6) = 45 and adm_rate(6) / adm_rate(5) = 1.2499293. Freezing the band at issue gives a year-6 claim of ₩150,937.05 against ₩183,428.50 — 17.71% low — and turns the projection’s only negative policy year into a comfortably positive one, which is the worst kind of error because it removes the one thing the projection had to say.

• lapse_rate is annual and lapse_rate_mth is monthly, and the library spells them apart for this reason. lapse_rate(0) = 0.10 against lapse_rate_mth(0) = 0.0087416110. Using the annual rate on the monthly grid takes pols_if(12) from 0.8898237107 to about 0.28.

• The renewal decline is not lapse and must not be folded into it. It is non-zero only where (t + 1) mod 12 = 0, it acts after mortality, lapse and suspension, and it is the larger of the two voluntary exits at every annual boundary — 0.0089881183 against 0.0079263524 at t = 11, and 0.0083529502 against 0.0043181413 at t = 23. Folding it into w(t) makes the annual boundary invisible, and on a contract whose whole architecture is annual that is the boundary the model exists to show. check_pols_roll_fwd() balances either way, so the roll-forward will not catch it.

• The 3대비급여 limbs never pass through the annual-limit factor. Their money caps replace the ₩50,000,000 aggregate for those three classes rather than sitting inside it [S1 특별약관 제3조(3) <표1>], so claims_np_three_pp(y) is summed apart from claims_np_main_pp(y) and np_limit_factor(y) is applied only to the latter. And where 3대비급여형 is not held those treatments are uncovered — they do not fall back into the main limit. Model point 6 is that election.

• reld_exempt_share reduces the rating count, never the benefit. claims_np_pp(1) = 62,978.2477 is paid in full; claims_np_rated_pp(1) = 0.85 × 62,978.2477 = 53,531.5106 is what the band is read against. The severely ill are exempt from the rating, not from the cover [S1 특별약관 제6조제3항] REG-R54. Applying the 15% to the claim would silently delete a fifteenth of the benefit.

• The 상급병실료 cap is a daily average, not a nightly cap. min(0.50 × charge, ₩100,000 × D) with D the whole admission’s length [S1 특별약관 제3조]. On the anchor the room payment is ₩135,000 over 7.5 days — ₩18,000 a day against a ₩100,000 cap — so the cap is slack by a factor of 5.6 and the largest capped point (0.50 × ₩1,200,000 = ₩600,000) sits below the ₩750,000 stay cap. A per-night implementation on a varying nightly charge pays strictly less; this model cannot show the difference because it holds only the admission total, and that limitation is stated rather than hidden.

• Do not delete a limit because it reads slack. check_annual_limits() is True on every shipped model point because E[min(X, Λ)] ≠ min(E[X], Λ) and a single cell’s expected annual claim is two orders of magnitude below every money limit — the supervisor’s own tail figure is 0.005% of insureds above ₩50,000,000 in 2019 R1. The check proves the machinery is wired, not that it is exercised, and every one of those limits binds under a seriatim or stochastic run.

• result_cf() publishes the five claim limbs and no claims subtotal. The columns must sum to net_cf with the three expense limbs, which is what check_net_cf() asserts; a subtotal column beside the splits invites a limb being counted twice invisibly. The claims(t, kind) cells stays, and claims(t) with no kind is the sum.

• expenses is maintenance only and claim_expenses is claim-driven. 7% of premium and 3% of claims respectively, on a std split of one published 16.1% aggregate R7. Folding the claim expense into expenses — or charging it on premium — makes a premium-driven cost and a claim-driven cost move together, and it breaks the two-term identity net_cf = 0.87 × premiums − 1.03 × claims that the whole shape of this projection rests on. check_expense_split() ties the three rates back to the published total.

• There is no acquisition strain, and inventing one is as wrong as omitting a real one. On a one-year renewable contract renewed on a rolling basis the acquisition/renewal distinction has no content after year one, so commissions(t) = 0.06 × premiums(t) is level and t = 0 is positive at ₩205.4984. A reader who expects the sister libraries’ month-0 trough will look for a bug that is not there.

• The two age conventions are both real and neither may be silently dropped. The model runs on 만나이 and the contract prices on 보험나이 [S1 제21조] REG-R25; the two differ for half of all issue dates, so half a year of age sits between the projection basis and the pricing basis. Model point 1’s issue_age = 40 is a 만나이.

• The premium is an input for policy year 1 only. premium_mth_pp() is prem_ge_base(1) + prem_np_base(1); every later year is the recursion. A model that re-reads the model point premium in year y > 1 throws away the entire renewal machinery, and on this cell would collect ₩1,066,375.5027 of premium over the 120 months instead of the projected ₩1,558,165.4328 — 31.6% less — while leaving the claim untouched, which turns a +₩118,476 result into a loss of about ₩309,381.