Technical Notes#

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

Scope note. These notes turn the standardized composite long-term-care insurance (ganbyeong boheom, 간병보험) of product-spec.md (same directory) into a reference liability cash-flow projection on paper, and then into LTC_KR_S beside it. They describe no single insurer’s contract. [S#] and [R#] tags resolve against sources.md, whose numbering is carried verbatim from _research/long-term-care.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 value here is identical to product-spec.md’s, and every number in the worked example is read off the shipped model rather than recomputed by hand.

Seven assumption inputs appear here that product-spec.md does not carry, because they are modelling constructs rather than contractual terms, and each is introduced below as such: the certification-prevalence curve by sex and 만나이; the prevalence-to-incidence conversion and its closing assumption direct_entry_share; the care-state and light-grade mortality multiples; the sub-65 gradient carried off the one disclosed 예정위험률; the grade-share vector by age band; the lapse level; and the expense and commission scales together with the 계약자적립액 reconstruction that drives the surrender-value cliff.

This document’s deltas against the cancer chassis#

This document states its deltas against the cancer technical notes (암보험), the krlib fixed-benefit (정액) 제3보험 chassis, whose model is Cancer_KR_S. That document specifies five mechanics once and in full — the diagnosis-triggered lump sum on a tier ladder, the 90일 면책기간, the 감액기간, the 유사암 reduced tier, and a post-diagnosis survival model — and this one does not restate them. It also settles, for the whole library, the 만나이 projection basis, the 표준약관 furniture (보험나이, 청약철회, 품질보증해지, 계약 전 알릴 의무, 납입최고, 실효, 부활), the statutory 계약자적립액 payable on a death the contract does not cover, the absence of a policy loan on a 미지급형 form, and the surrender-value regime of 감독규정 제7-65조 through 제7-68조 as extended to 제3보험 by 제7-69조 and 제7-70조 REG-R19.

Six things change, and five of them change the shape of the model rather than a parameter in it.

  1. The trigger is a statute’s, not a classification’s — and it is a state, not an event. The chassis reads a KCD code that a pathologist assigns and an insurer applies. Here a 등급판정위원회 sitting inside 국민건강보험공단 scores an applicant on a 52-item instrument and awards a 장기요양등급, and the 지급사유 is written by reference to that award and to nothing else [S1] [S2] [S3] [S4]. The statutory definition carries its own six-month duration test — 「6개월 이상 동안 혼자서 일상생활을 수행하기 어렵다고 인정되는 자」 REG-R54 제2조제2호 — so the contract needs no persistence clause of its own, and the point thresholds live in a 대통령령 that can be moved without reference to any insurer REG-R55 제7조제1항.

  2. Four compartments, not three, and the middle one is where the claims come from. The chassis carries a never-diagnosed state, a 특정소액암 state that still pays premium and a waived state that does not. This model carries a never-certified state, a light-grade state (3~5등급 and 인지지원등급, below the contractual threshold) that still pays premium and still lapses, and an absorbing care state that pays neither. The parallel is exact and it is not a coincidence: in both products the waiver fires at a threshold above the first insured event, so there is a diagnosed population the contract has not yet started paying for. What is new here is that the middle compartment is the dominant route into the benefit: only 13.3% of current 1등급 certifications arose from a first application, against 69.5% from a renewal, whereas at 인지지원등급 — a grade nobody progresses down into — the first-application share is 69.8% R4 표2-5. Severe-grade lives are, in the main, people who entered the scheme years earlier at a light grade and deteriorated.

  3. The chassis’s incidence basis is sourced; this one’s is a prevalence and has to be converted. 보험개발원 publishes a dated 「기타피부암 및 갑상선암 이외의 암 발생률」 grid by age and sex on its 장기손해보험 참조순보험요율 display REG-R61, so Cancer_KR_S reads an incidence directly and spends its judgement on the tier decomposition of it. No Korean body publishes a long-term-care incidence table at all. What is published is the 국민건강보험공단 노인장기요양보험 통계연보’s 연령별 인정률 R4, and an 인정률 is a prevalence — a point-in-time count of people holding a certification. The conversion is the modelling work of this product, it needs the mortality of the care state inside it, and it is done in the open in section (c) below rather than replaced by an assumed incidence rate.

  4. The post-onset survival model is the product, not a correction to it. On the chassis, survival after diagnosis decides how long the waiver, the inpatient limb and the treatment limb run — real, but second-order against a lump sum paid on day one. Here the 간병연금 is metered month by month on survival in the care state for up to ten years, the waiver stops the premium for as long as that state lasts, and — this is the part with no chassis counterpart — the same care-state mortality multiple is also a term of the incidence identity, so it moves entry and run-off in opposite directions at once. There is no number in this model that does not depend on it.

  5. No reduced tier; a threshold ladder instead. The chassis’s 유사암 tier covers a high-frequency, high-survival decrement at a fraction of the general amount without repricing. There is no analogue here. The light grades are reached by moving the threshold — 1등급 / 1~2 / 1~3 / 1~4 / 1~5 / 1~인지지원등급, always cumulative from the top — which is a different product at a different price, about 4.5 : 1 between 1~5등급 and 1~2등급 at the same 가입금액 [S2, derived], not a fraction of this one. The threshold is a model point field, and widening it changes the frequency and the timing together.

  6. Two parameter-level deltas. The 예정이율 is sourced here at 연단위 복리 2.0% [S1] against the chassis’s std 2.50%, because one carrier states it in terms in a 기초서류 extract; it is a 2023-vintage 우정사업본부 rate and the three cautions travel with it (see (b) below). And the 표준해약공제액 is taken from the supervisor’s 13-months-of-premium rule of thumb REG-R29 rather than from the chassis’s notional_sa_ratio route through [별표 15] 제9호, because 제9호’s own third bullet excludes 「치매 또는 일상생활장해 등 타인의 간병을 필요로 하는 상태」 risk premium from the ratio that gives a contract with no death benefit its notional 보험가입금액 REG-R21. Read literally, the formula the chassis inherits excludes long-term-care risk premium from the very quantity a long-term-care contract needs.

Everything else is the chassis’s and is not restated: 무배당 with no policyholder dividend REG-R12; a fixed sum (정액) paid on an event rather than an indemnity against a cost; a benefit payable 최초 1회한 that extinguishes the benefit line paying it without terminating the contract; the 해약환급금 미지급형 form with its cliff at 납입완료; the 계약자적립액 on non-covered death REG-R17 REG-R25 제22조 REG-R50 제736조; and the absence of a 보험계약대출 and therefore of any automatic premium loan REG-R28.

One product this document is not about. Korean commentary in 2024–2025 uses 간병 overwhelmingly to mean 간병인사용일당, a hospital-days indemnity whose loss ratios reached about 100% in the life sector at August 2024 against 18.7% two years earlier R15, news. It sits inside the same 약관 [S1] [S2] [S4] and shares nothing else; LTC_KR_S does not model it.

Model scope and conventions#

  • Purpose. Project gross best-estimate liability cash flows for a single-policy model point of 간병보험: office premiums; the 장기요양진단급여금 on first award of a grade at or above the contractual threshold; the 간병연금 metered by an annual survival test; the optional 치매진단급여금; the 계약자적립액 paid on a death from a cause the contract does not cover; the 해약환급금 paid on surrender; the premiums returned where a certification inside the 보장개시일 window makes the cover 무효; maintenance and claim-handling expense; and commission. 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 from the same quarter REG-R13; and the 해약환급금준비금, which has no counterpart anywhere else in this repository REG-R11. 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, and monthly by construction rather than by approximation. 월납 is the dominant retail mode and the mode of every published rate card in the file [S1] [S2]; the 90-day 보장개시일 lands on the grid boundary t = 3; the one-year 감액기간 lands on t = 12; and — the mechanic that forces the grid — the 간병연금 instalment is monthly while its survival test is annual, so a model on an annual grid cannot represent the twelve-month guarantee at all. t is the policy month and it is 0-based: t = 0 is the first projected month, t = 0, 1, …, n − 1 with n = proj_len(); month t is the interval from t to t + 1 months after the 보험계약일; and the contractual policy year is the derived 1-based label y(t) = floor(t / 12) + 1.

  • proj_len() is the number of projected months, the frame’s exclusive end — not the last index. proj_len = 12 × (term_age − issue_age) + 1, so 601 on the anchor cell and 601 rows in result_cf(), indexed t = 0 … 600; the frame is range(proj_len()) and the last index is proj_len − 1. The + 1 is the terminal row: the 600 months of cover are t = 0 … proj_len − 2, and month t = proj_len − 1 is the 90세 계약해당일 itself, which carries the surviving in-force count, pols_maturity records the cover ending, and every cash flow on that row is zero — 「이 상품은 순수보장성보험으로 보험계약 만기시 지급받는 금액(만기환급금)이 없습니다」 [S3].

  • The waiting period lands on a grid boundary. The 장기요양상태 보장개시일 is 「계약일(부활(효력회복)계약의 경우 부활(효력회복)일)부터 그 날을 포함하여 90일이 지난날의 다음 날」 [S2]. On a monthly grid that is three whole months, t = 3 std, and the model claims no finer precision. A certification inside the window does not defer the claim: the benefit is 무효 and the premiums paid for it come back [S1] [S2]. This is the chassis’s mechanism with the chassis’s consequence, but without the chassis’s option — Cancer_KR_S lets the policyholder cancel the rest of the contract within 90 days of the 진단확정일 [S1 of that product], and no retrieved long-term-care contract has any equivalent, nor any revival clause.

  • Timing conventions std. Office premium received at the start of month t, and only by lives not on 납입면제; maintenance expense at the start of month t; the lump sum, the annuity instalment, the dementia benefit, the 계약자적립액 on death, the 해약환급금 on lapse, the refund on a voided cover and the claim-handling expense at the end of month t; decrements at the end of month t, in the order certification, then mortality, then lapse. Acquisition expense and initial commission at t = 0.

  • Claim-date convention std. Every claim is dated at the month the 판정일 falls in. The determination is due within 30 days of the application, extendable by a further 30 R3, citing 법 제16조제1항. The 보장개시일 test is measured to the 판정일, so a model dating the claim at the application would let a certification through the window the contract voids.

  • The annuity’s first instalment falls in the month of certification — 「진단 확정된 날을 최초로 하여 10년 동안 매년 진단 확정일에 살아있을 때」, 「최초 1년(12개월) 보증지급」, 「10년(120개월)을 최고한도로 지급」 [S1]. The u = 0 term of the ledger is the entrant cohort itself; there is no deferral.

  • Age basis. 만나이 (man nai, age last birthday), incremented on the policy month grid: age(t) = x + floor(t / 12). The contract ages on 보험나이 (boheom nai): 「계약일 현재 피보험자의 실제 만 나이를 기준으로 6개월 미만의 끝수는 버리고 6개월 이상의 끝수는 1년으로 하여 계산」 REG-R25 제21조, and the two differ for roughly half of all issue dates. The 만나이 basis is not a concession here, as it is on the chassis; it is the right basis twice over. Every public series this model’s decrements are built from is published on 만나이 — the 통계연보 연령별 인정률 R4, the 치매역학조사 prevalence R7, and the 생명표 behind the mortality REG-R38 REG-R39 — and the benefit definition itself contains a 만나이 test: 「만 65세 이상 노인」 또는 「노인성 질병을 가진 만 65세 미만의 자」 [S2] REG-R54 제2조제1호. The 보험나이 offset therefore survives only in the premium, which enters this model as an input, so no conversion is applied anywhere. The direction is nonetheless stated: the disclosed 예정위험률 the conversion is calibrated against is quoted on 보험나이, about half a year older than this model’s 만나이, which is one of the four reasons the calibration ratio in (c) sits below one.

  • Currency. KRW throughout. There is no minor unit in the contract, but expected values are fractional; displayed to the precision each table states.

  • Model points. One policy at a time, projected on an expected (probability-weighted) basis. Projection is parameterized by point_id; no aggregation logic is specified here. Nine points are shipped and every one satisfies every check_*() cells.

  • Termination. Cover to the 90세 계약해당일, t = proj_len − 1. The decrements are death, lapse, the voided cover of the waiting-period window, and maturity — and nothing else. There is no benefit-driven termination: payment of the 진단급여금 extinguishes that benefit line and leaves the contract, the annuity and the dementia rider running [S1] [S2] [S3] [S4].

  • Contract boundary. The long-term-care benefit is written 비갱신형 on every document retrieved [S1] [S2], with a level premium, 무배당, and no insurer repricing right on the benefit, so every future premium and benefit is inside the boundary and the horizon is the whole term. That is the opposite of the Korean medical market, where annual renewal is the defining feature, and it is the right answer for a benefit whose claim arrives thirty years after issue: a renewable long-term-care rider re-rated at attained age would price itself out of existence exactly when it was needed. The renewable form is not modelled.

  • Rounding. Intermediates at full double precision. The worked example displays policy counts to ten decimals, first-year cash flows to six, milestone rows to four and aggregates to four. Monthly rows rounded for display do not re-add to the displayed totals; the totals are sums of unrounded values.

  • What this model is not. It is a mechanics demonstration. The premium is a model point input, the whole morbidity basis is a construction from public administrative statistics, the post-onset mortality basis is std with no published table behind it anywhere, and the expense scales are std. Replace the assumption tables with company data before drawing any conclusion from the output.

Model point attributes#

Attribute

Type

Anchor cell (point_id = 1)

policy_id

str

LTC-000001

issue_age (x)

int, 만나이, 30–70

40

sex

enum {M, F}

M

term_age

int, 만기나이

90

prem_period_years (n_Y)

int years, 납입기간

20

prem_mode

enum {monthly}

monthly (월납)

benefit_grade (G_B)

enum {g1, g2, g3, g4, g5, g6}

g2 — 장기요양 1~2등급

lump_amount (A_B)

보험가입금액, KRW

10,000,000 (1,000만원)

annuity_on

bool — the 간병연금 rider

True

annuity_high (A_1)

KRW per month at an entry grade of 1등급

500,000

annuity_low (A_2)

KRW per month at any other grade in the gate

300,000

annuity_max_mths (n_A)

int months, the 최고한도

120

annuity_guar_mths

int months guaranteed against death

12

dementia_rider

bool — the 치매진단급여금 rider

False

dementia_amount

KRW (rider off on the anchor)

10,000,000

wait_mths (W)

int months, 장기요양상태 보장개시일 on the grid

3

red_mths (G)

int months, 감액기간 ∈ {0, 12, 24}

12

cv_form

enum {mijigeup, half_during, pyojun}

mijigeup (해약환급금 미지급형)

lapse_form

enum {mujihae, pyojun}

mujihae

uw_loading

float — the 간편심사 premium multiplier

1.0 (일반심사)

premium (P)

KRW per month, office premium, model-point input

5,600 std

Derived scalars on the anchor cell, all read off the model: proj_len() = 601, prem_period_mths() = 240, premium_mth_pp() = 5,600.0, pols_if_init() = 1.0, net_prem_ratio() = 0.7931662309087683, comm_init_pp() = 43,680.0 and sub65_gradient() = 0.12221178050285361.

premium is an input, not a computed quantity, and the reason is the same as on the chassis with one aggravation. No Korean carrier publishes a long-term-care rate card at the composite’s specification: the 산출방법서 and the 사업방법서 are 기초서류 filed with the FSC and are not public REG-R2, and the one published card [S2] quotes covers that do not match the composite one for one. The anchor is therefore constructed from two rows of that card, both at 90세만기, 20년납, 월납, 일반심사형, 보험가입금액 1,000만원: ₩3,300 for the 주계약 장기요양(1~2등급)급여금 at male 40, plus ₩580 for the 장기요양(1-2등급)재가급여종신지원특약 which pays ₩100,000 a month on the same trigger, scaled to the composite’s grade-weighted ₩400,000 a month — ₩2,320 — giving ₩5,620, rounded to ₩5,600 std. The female cell is ₩5,000 + 4 × ₩850 = ₩8,400 [S2, derived]. Two offsetting differences are recorded rather than adjusted for: the [S2] rider runs 최대 종신 where the composite caps at 120 months (dearer), and it requires the insured to be using 재가급여 in the month where the composite tests only survival (cheaper).

On this model’s own basis the anchor premium is not far wrong. The present value at the 예정이율 of 2.0% of the anchor cell’s long-term-care benefit outgo is 46.03% of the present value of premium income, and the present value of expenses, claim expenses and commission is 20.26%, against the 20.68% loading that net_prem_ratio() implies from the published 환급률 progression. Read that pair carefully. The 20.26% is calibrated to the 20.68% — expense_maint is set to land near it (see (c) below) — so their agreement is a construction and the 0.42-point gap is the rounding of expense_maint to a whole ₩200. What is not calibrated is the 46.03%. Nothing ties the incidence basis, built from the 통계연보 R4, to the premium, built from a rate card [S2]; that a benefit ratio of 46% and a loading of 21% together leave the contract close to self-supporting at the disclosed 예정이율 is the finding here, and it is the one figure two unrelated documents had to agree on without being made to.

The eight other model points exercise both sexes, issue ages 30 to 70, all six thresholds from 1등급 to 1~인지지원등급, 90 / 95 / 100세만기, 10 / 20 / 30년납, the three surrender-value forms, the 간병연금 on and off, the 치매 rider on and off, the 간편심사 loading, the 우체국 180-day waiting period with its two-year 감액, and the 표준형 lapse comparison vector. Model point 8’s positive net_cf is an artefact and is described as one in Key sensitivities below.

State variables#

Variable

Description

Updated

pols_healthy(t) (h)

In force at the start of month t and never certified; pols_healthy(0) = pols_if_init()

monthly recursion

pols_light(t) (l_L)

In force and certified at a grade below benefit_grade(); pols_light(0) = 0

monthly recursion

pols_care(t) (l_C)

In force and certified at or above benefit_grade(); absorbing; pols_care(0) = 0

monthly recursion

pols_act(t)

pols_healthy + pols_light — the premium-paying, lapse-exposed population

derived

pols_if(t) (l)

pols_act + pols_care — total in force at the start of t

derived

pols_healthy_mid(t), pols_light_mid(t), pols_care_mid(t)

The three counts after the month’s certifications, before mortality

derived

pols_dem(t)

In force and already paid the 치매진단급여금; a first-event counter, not a compartment

monthly recursion

av_pp(t) (AV)

계약자적립액 per policy at the start of month t

two-branch recursion

cv_pp(t) (CV)

해약환급금 per policy paid on a lapse in month t

derived

age(t)

Attained 만나이 = x + floor(t / 12)

annually

mort_rate(t), mort_rate_light(t), mort_rate_care(t)

Annual mortality of the three compartments at age(t)

lookup / derived

prev_rate_at(x) (P)

All-grade certification prevalence at 만나이 x

fitted logistic

prev_care_at(x) (P_C), prev_light_at(x) (P_L)

Prevalence at or above, and below, benefit_grade()

derived

inc_rate_direct_at(x) (i_D)

Annual direct entry rate, healthy → care

derived

inc_rate_light_at(x) (i_L)

Annual entry rate, healthy → light grade

derived

prog_rate_at(x) (rho)

Annual progression rate, light grade → care

derived

lapse_rate_mth(t) (w)

Monthly lapse, applied to pols_healthy and pols_light only

derived

red_factor(t) (r)

The 감액 factor applying to a certification dated in month t

derived

ann_amount_at(s) (A(s))

The monthly 간병연금 of the cohort certified in month s, frozen at entry

derived

net_cf(t) (CF)

Net cash flow of month t, insurer perspective, income-positive

monthly

Why four compartments and not three. The chassis’s three states are forced by its waiver clause; ours are forced by the certification statistics. A light-grade life is certified — the state is real, and it carries impaired mortality — but the contract does nothing for it: no benefit, no waiver, no annuity, and no retrieved Korean contract pays anything at a grade below the stated threshold. So a light-grade life keeps paying premium and stays exposed to lapse, exactly like the chassis’s 특정소액암 life, and it is the pool progression draws from. On the composite’s 1~2등급 gate the light compartment is about six sevenths of all certified lives: 1·2등급 are 13.28% of the 1,165,030 certified at end-2024 R4 표2-5, derived. Collapsing the two either stops a premium the contract goes on charging or invents a benefit at a grade the contract does not cover, and — the larger error — it makes the severe-grade entry rate a healthy-life incidence, which puts the cash flow years too early.

The care compartment is absorbing, and the contract is drafted so that it is. The 진단급여금 cannot be re-triggered [S1] [S2] [S3] [S4]; the 간병연금’s amount is fixed by the grade at first certification and 「그 이후에 장기요양등급이 변경되더라도 지급액은 변경되지 않습니다」 [S1]; the instalments are metered on survival, not on continued certification [S1]; the premium is waived [S3]; and surrender is barred — 「최초 지급사유가 발생한 후에는 이 특약을 해지할 수 없습니다」 [S1]. So no recovery, no downgrade and no lapse in the care state are a property of the contract before they are an assumption of the model. That is worth saying plainly, because grades genuinely move both ways — 107,365 of the 1,165,030 current certifications arose from a 등급변경신청 R4 표2-5 and one carrier drafts a rider around exactly that [S3] — and a model of a utilisation-conditioned benefit could not make this simplification at all. See Key sensitivities.

The dementia counter is nested, never added. pols_dem(t) rides on the in-force block and is held at or below pols_if(t) so that pols_entry_dem always draws from a non-negative pool. It is a first-event ledger on the same lives, not a fifth compartment. Driving it off a sourced dementia prevalence R7 rather than off a share of the certification rate is deliberate: the two triggers are correlated but not proportional — dementia is the sole qualifying condition for 5등급 and 인지지원등급 REG-R55 제7조제1항 and is present in 42.3% of certified decedents R11, yet most CDR 1 lives are nowhere near a 1·2등급 certification.

Three absences are product facts, not gaps. There is no death benefit [S1] [S3], so claims_death is a return of the 계약자적립액 and not a sum assured. There is no 보험계약대출 and no automatic premium loan during the 납입기간 on the 미지급형 form, because there is no surrender value to lend against REG-R25 제33조 REG-R28 — a missed premium really does lapse the contract at the end of the 14-day 납입최고. And there is no 만기환급금: claims(proj_len − 1, "MATURITY") is zero and the column exists only so that the statement’s shape matches the rest of the library.

Assumption inputs#

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

Input

Value

Basis

Trigger

Award of a 장기요양등급 at or above benefit_grade() by the 등급판정위원회 under 노인장기요양보험법; no company-basis limb, no ADL schedule, no persistence clause

[S1] [S2] [S3] [S4]; REG-R54 제15조

Eligibility gate

「만 65세 이상 노인」 or a person under 65 with one of the 25 노인성 질병 the 시행령 [별표 1] lists

[S2]; REG-R54 제2조제1호 REG-R55

Grade point bands

1등급 95점 이상 · 2등급 75~95 · 3등급 60~75 · 4등급 51~60 · 5등급 45~51 (치매 한정) · 인지지원등급 45점 미만 (치매 한정)

REG-R55 제7조제1항; R3; reproduced in a carrier’s own document [S2]

장기요양진단급여금

A_B = ₩10,000,000, 최초 1회한 on the first award at or above the threshold on or after the 보장개시일; extinguishes that benefit line, not the contract

[S1] [S2] [S3] [S4]; threshold std

장기요양상태 보장개시일

「계약일…부터 그 날을 포함하여 90일이 지난날의 다음 날」, t = 3 on the grid, with a carve-back to the 계약일 where the cause is 재해

[S2]; std, observed range none / 90 / 180 days

Pre-inception certification

The affected cover is 무효 and the premiums paid for it are returned; no cancellation option and no revival

[S1] [S2]

감액기간

1 year at 50% where the cause is 질병; the full amount where the cause is 상해/재해

[S4]; length std, observed none / 1yr / 2yr

The 감액 is frozen

The reduction decision is fixed at first certification and does not change as later instalments fall outside the window

[S1]

간병연금

Monthly from the 진단확정일: ₩500,000 where the entry grade is 1등급, ₩300,000 otherwise; annual survival test on each anniversary of the 진단확정일; first 12 months guaranteed; 120 months maximum

[S1]; shape std

Annuity amount frozen

Set by the grade at first certification and never re-rated — 「그 이후에 장기요양등급이 변경되더라도 지급액은 변경되지 않습니다」

[S1]

Annuity on death

The stream stops; where death follows a paid instalment no 책임준비금 is returned

[S1]

Surrender after the annuity starts

Barred — 「최초 지급사유가 발생한 후에는 이 특약을 해지할 수 없습니다」

[S1]

Proof of life

「매년 진단 확정일에 피보험자의 주민등록등본을 제출하여야 합니다」 — an annual administrative event

[S1]

보험료 납입면제

On the award of 1등급 or 2등급, waiving the 기본계약 and every attached rider; waived premiums treated as paid

[S3]; threshold std

치매진단급여금

Optional: ₩10,000,000 on the first 최종진단확정 of CDR 1 이상, once only across the tier set, behind a one-year 보장개시일 and the definition’s own 90-day persistence test

[S2] [S4]; tier std

Payment on non-covered death

The 계약자적립액 at the date of death plus unearned premium, whereupon the contract ends

REG-R17 REG-R25 제22조; REG-R50 제736조

General death benefit

None

[S1] [S3]; std

만기환급금

None — 「이 상품은 순수보장성보험으로 …」

[S3]

Surrender value form

미지급형: 0% during the 납입기간, 50% of the notional 기본형 value afterwards

[S2]; REG-R19 제7-66조제4항

해약환급금 floor

max(계약자적립액 − 해약공제액, 0); the 해약공제액 may not exceed the 표준해약공제액 of [별표 14]; 해약공제기간 = 납입기간 capped at 7 years

REG-R19 제7-66조제1항; REG-R20

계약자적립액 accrual

Monthly before 납입완료, daily afterwards; permitted to be computed on an annualised premium basis

REG-R19 제7-66조제1항제4호; REG-R18 제7-65조제2항

Refusal on a defective certification

Where the grade was obtained by 허위 또는 부당 판정, nothing is paid; and where the public benefit is restricted under 노인장기요양보험법 제29조

[S1] [S2] [S4]

납입최고 (grace)

At least 14 days; the contract terminates the day after the 납입유예기간 ends

[S1]; REG-R25 제26조

부활

Within three years; the 보장개시일 clock restarts from the 부활일

[S1]; REG-R25 제27조

Expiry

At the 90세 계약해당일; nothing is paid

[S3]

The statutory-change clause, which has no chassis counterpart and is not modelled. No retrieved contract gives the insurer a 기초율변경권 on the long-term-care benefit. What it gives instead is a contract-continuity provision: where the statute is amended so that the grades cease to exist or cease to be determinable, the insurer 「객관적이고 합리적인 범위 내에서 기존 계약내용에 상응하는 “장기요양상태”와 관련된 새로운 보장내용으로 이 계약의 내용을 변경합니다」 [S3], and the definition itself names a successor body 「향후 제도변경시 에는 동 위원회와 동일한 기능을 수행하는 기관」 [S4]. Neither is a repricing right. The asymmetry is the central risk of the Korean product and it is real: the 인지지원등급 was created out of nothing on 2018-01-01 R6 and enlarged the covered population of every 「1~인지지원등급」 rider overnight, at no additional premium. LTC_KR_S models the basis that exists and carries the risk as a stated model risk, not as a parameter.

(b) Insurer-discretionary current elements#

This class is nearly empty, and its emptiness is the product fact — the same position as the chassis, and for a stronger reason. The composite is 무배당 wherever the dividend basis is stated [S1] [S2] [S3] [S4], so there is no 계약자배당 and the surplus-distribution machinery of 감독규정 제6-11조의7 and 제6-13조 does not attach REG-R12. The design is 금리확정형, so there is no 공시이율 to reset and no 최저보증이율 to bind. There is no premium review on the 비갱신형 chassis and no MVA. What remains:

Input

Snapshot value

Basis

예정이율 / 계약자적립액 적용이율

2.0% 연단위 복리, 금리확정형 — 「무배당 우체국간병비보험 2309의 주계약 및 특약에 적용한 예정이율은 연단위 복리 2.0%입니다」

Sourced [S1] — the only Korean long-term-care 예정이율 in any retrieved document

Incidence basis in the filed rate

The insurer’s own, in the 산출방법서, a 기초서류 filed with the FSC and not published

REG-R2

간편심사 pool

A premium multiplier of 1.36–1.43× on the main contract [S2, derived]; the pool’s own incidence is in no source

multiplier sourced; incidence std

지정대리청구인

Always designated; up to two, one as 대표대리인. No cash-flow effect and a mandatory operational feature of a product whose claimant usually cannot claim

[S1] [S3]

장애인전용보험전환특약

Raises the tax credit from 12% to 15% where the insured or beneficiary is a 소득세법 장애인; policyholder-side, not modelled

[S1] [S2]; REG-R57

Three cautions travel with the 2.0%, and they are why it is the one place in krlib where a sourced number is arguably weaker than a std one would be. It is a 2023-vintage rate on a 2309 product, and the 예정이율 moves with the market. It is a 우정사업본부 rate, and 우체국 insurance is written outside 보험업법. And it prices a different benefit mix: 우체국’s 주계약 pays a 재해사망보험금 and the long-term-care covers are riders on it. It is nonetheless preferred to an invented figure — and at 2.0% against the chassis’s std 2.50% the composite is the more conservative of the two on a benefit payable forty years out. Note also that a full-text search of the 감독규정 returns zero occurrences of 예정이율 REG-R9: the regulation speaks only of the 계약자적립액 적용이율 and of the 금리확정형 / 금리연동형 distinction REG-R48, so the 예정이율 of a specific Korean product is not a published number for any other product in this library.

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

Mortality of the never-certified. mort_table.csv is a construction, not a copy. 경험생명표 (제10회, applied from 2024-04) is produced by 보험개발원 and is not released in full: what is published is the 평균수명 and the 기대여명, not the rates REG-R33 REG-R34. What is shipped is a Makeham–Gompertz

q(x) = 1 − exp( −( A + B c^x ) )                                            [std]

with A = 0.0003 std and c = 1.10 std, and B solved per sex so that the complete expectation of life at 65 reproduces the published 제10회 경험생명표 65세 기대여명 — 23.7 years for men and 27.1 for women REG-R33. That gives B = 1.494698342e-05 (M) and 1.018884285e-05 (F), with a terminal age of 120 where q = 1. The construction is not fitted to anything else and it reproduces the second published summary statistic without being asked to: the implied 평균수명 at issue age 40 is 86.4 for men against the published 86.3, and 90.3 for women against 90.7. That is a cross-check on the shape, not evidence about any insurer’s experience, and no conclusion about Korean insured mortality should be drawn from the file.

mort_rate_mth(t) = 1 − (1 − q(age(t)))^(1/12) std. There is no best-estimate adjustment factor: the calibration anchor is an experience statistic, not a valuation table with a prudential margin, so there is nothing to unwind.

This is a delta against the chassis and it runs the right way. Cancer_KR_S calibrates its Makeham on the population 생명표’s 기대여명 at 40 and 65 REG-R38 — 19.5 years at 65 for a man. This model calibrates on the insured table’s 23.7 at the same age, so its healthy lives are materially lighter than the chassis’s. On a product whose benefit is a living one that is the conservative direction: longer survival means more entrants into the care state and more annuity instalments once there. On a cancer contract the same choice would be the other way round. Both are std and both say which table they used; a reader comparing lifetime claim rates across the two products should not read the difference as experience.

Care-state and light-grade mortality — the multiples, and where they come from. No retrieved source publishes a post-certification mortality table by grade, and 보험개발원 publishes neither a 장기요양 incidence table nor a post-onset mortality table at all. The model carries flat multiples:

mort_rate_care(t)  = min(1, care_mort_mult  × q(age(t))),   care_mort_mult  = 3.0  [std]
mort_rate_light(t) = min(1, light_mort_mult × q(age(t))),   light_mort_mult = 1.8  [std]

care_mort_mult = 3.0 is derived rather than assumed, from two sourced quantities. The yearbook roll-forward and the application-route estimator agree that the mean duration of a certification is near 4 to 5.5 years (see the conversion below), and the mean 만나이 of a certified decedent is over 75 R11. At 만나이 82 on the shipped table a mean duration of 4.5 years implies a force of 0.222 against a healthy force of 0.075 — a multiple of 2.96. The one retrieved study measuring time from certification to death — 516.2 days, 8.7% inside a month, 45.6% inside a year, on 271,474 people R11 — is a right-censored decedent cohort: only people who died inside a 4.5-year observation window are in it, so everybody with a long duration is excluded by construction. It is a lower bound on the mean duration and it fixes the early shape here, not the level.

light_mort_mult = 1.8 has no source and no observed range. It is bounded above by the care multiple and below by unity, and R11’s mean 인정점수 at death of 82.1 — squarely inside 2등급 — says the deaths of that cohort are concentrated in the severe grades, so a light-grade life is materially healthier than the cohort the study observed.

care_mort_mult is not only a post-onset assumption. It is also the excess-mortality term of the incidence identity below, so it moves the entry rate and the annuity’s run-off in opposite directions at once. That coupling is the least obvious property of this model and it is varied in a sensitivity rather than described.

Prevalence to incidence — the conversion, shown rather than assumed#

The published quantity is a prevalence. The 2024 노인장기요양보험 통계연보’s 연령별 인정률 counts people holding a valid certification at a point in time, not people entering one R4 표2-9, 표1-2, derived:

연령

인정자

인구

인정률 (T)

인정률 (남)

인정률 (여)

65–69

66,955

3,715,757

1.80%

1.98%

1.63%

70–74

102,751

2,437,413

4.22%

3.95%

4.45%

75–79

176,578

1,796,342

9.83%

7.45%

11.76%

80–84

320,148

1,344,376

23.81%

15.45%

29.24%

85+

461,622

1,105,925

41.74%

28.63%

47.31%

65+

1,128,054

10,399,813

10.85%

6.87%

14.02%

Two features of the sourced curve survive everything below and both matter. The gradient is about 17.0% per year of age — a factor of 23 over twenty years. And the sex crossover is at about 70: male certification exceeds female below it and female exceeds male above, which is the reverse of a death-benefit table and is independently confirmed by the disclosed 예정위험률, whose female-over-male ratio runs 0.357 at 40, 0.575 at 50 and 0.882 at 60 and therefore crosses one in the late sixties [S1, derived]. The disclosed pricing basis and the national statistics agree on the sex crossover to within a few years, which is the strongest internal consistency check available.

Step 1 — a prevalence curve by age and sex std. A three-parameter logistic

P(x) = prev_ceil / ( 1 + exp( −prev_beta × (x − prev_x_mid) ) )             [std]

least-squares fitted in log space through the five sourced band rates at representative ages 67 / 72 / 77 / 82 / 88.5, the last being the population-weighted mean age of the 85+ band std. Male (0.7480, 0.14692252, 91.61515338); female (0.6310, 0.22384681, 83.31342651). Fit residuals are within ±5.2% (M) and ±7.9% (F). The derivative used below is the analytic one,

P'(x) = prev_beta × P(x) × ( 1 − P(x)/prev_ceil )

and not a difference quotient: P' is the leading term of the incidence identity, and a numerical derivative would put fitting noise straight into the claim rate.

Nothing above 88.5 is sourced. The logistic has three parameters and five anchors, so the fit is over-determined and the ceiling is identified in a way the chassis’s is not — but it is identified by extrapolating five points that stop at 88.5, and on this composite the projection stops at 90 anyway. The sensitivity in Key sensitivities shows the consequence, and it is a smaller one than in the Japanese counterpart for exactly that reason.

Step 2 — the grade share, by age and not by all ages std. share_ge_at(G, x) is the share of certified lives at grade G or above, linear in age between six sourced band representative ages — 60 standing for the whole under-65 band std, then 67, 72, 77, 82 and 88.5 — and flat outside them R4 표2-9, derived. It is a proportion of a population, never a rate. Then P_C(x) = share_ge_at(G_B, x) × P(x) and P_L(x) = P(x) − P_C(x).

Carrying the share by age is load-bearing, because the severe share is U-shaped:

연령

1등급

2등급

3등급

4등급

5등급

인지지원

1·2등급 계

<65

11.7%

10.5%

30.3%

36.1%

8.7%

2.7%

22.3%

65–69

6.5%

8.1%

26.8%

45.5%

10.0%

3.0%

14.6%

70–74

5.2%

7.5%

25.7%

46.6%

11.8%

3.2%

12.8%

75–79

4.3%

7.1%

24.4%

47.1%

13.6%

3.4%

11.4%

80–84

3.8%

7.3%

24.6%

47.6%

14.0%

2.8%

11.1%

85+

4.7%

10.1%

28.9%

45.3%

9.7%

1.4%

14.8%

The under-65 population is severe because only the 노인성 질병 list gets in at all REG-R55; the 80–84 trough is where the scheme’s marginal entrant is a lightly impaired person newly crossing the 51-point line; the 85+ rise is genuine deterioration. The shipped share_ge for g2 below 65 is 0.222, the sum of the two rounded grade shares in that row; R4’s own derived 1·2등급 계 is 22.3%, and the tenth of a point between them is rounding inside the source table rather than a second basis. A model applying a single all-ages vector at every age is wrong by up to a factor of two — 22.2% against 11.1% between the ends — and it is wrong at exactly the two ages that matter, the issue age and the claim age.

The derivative of P_C is taken by the full product rule,

P_C'(x) = s_G'(x) × P(x)  +  s_G(x) × P'(x)

with s_G' the exact constant slope of the bracketing linear segment. The first term is negative over most of the range for a severe threshold, and dropping it overstates the inflow badly: at 만나이 65 the second term alone is 1.82× the correct P_C', and at 75 it is 1.19×.

Step 3 — the identity, which carries the care state’s own mortality in it. Write mu_H, mu_L, mu_C for the three forces of mortality — mu(x) = −ln(1 − q(x)), in forces and not in annual rates, because the excess-mortality term is a difference of hazards and a rate difference is not one — and

mu_bar(x)   = (1 − P) mu_H  +  P_L mu_L  +  P_C mu_C
inflow_C(x) = max( 0,  P_C'(x)  +  P_C(x) × ( mu_C(x) − mu_bar(x) ) )
inflow_L(x) = max( 0,  P_L'(x)  +  P_L(x) × ( rho(x) + mu_L(x) − mu_bar(x) ) )

The second term is not a refinement. A rising prevalence understates entry, because the compartment it measures is simultaneously being drained by an excess mortality the population around it does not carry. At 만나이 65 the slope term is 83.8% of the inflow and the mortality term the other 16.2%; at the ages where the claims actually arise the mortality term is a larger share still. And mu_bar rather than mu_H is what turns a count identity into a proportion identity — prevalence is measured against a living population, and a population that is itself dying faster raises every prevalence it measures. Using mu_C alone in place of mu_C − mu_bar inflates the inflow at 65 by 8.2%, and by more at older ages.

Step 4 — the closing assumption. Two equations carry three unknowns: direct entry, progression, and light-grade entry. The closing assumption is the one the sources leave genuinely open, direct_entry_share = 0.20 std — the share of gross inflow into the care state arriving straight from health rather than by progression:

i_D(x)  = direct_entry_share × inflow_C(x) / ( 1 − P(x) )
rho(x)  = ( 1 − direct_entry_share ) × inflow_C(x) / P_L(x)     [0 where P_L = 0]
i_L(x)  = inflow_L(x) / ( 1 − P(x) )

Its anchor is the yearbook’s own application-route table R4 표2-5: 13.3% of current 1등급 certifications arose from a first application (7,371 of 55,340) against 69.5% from a renewal, whereas at 인지지원등급 — a grade nobody progresses down into — the first-application share is 69.8% (19,436 of 27,835). The ratio of the two is where 0.20 comes from. Getting it wrong does not change the lifetime claim count much; it changes when the claim arrives, which on a contract priced at 2.0% over fifty years is most of the answer. Where the gate is g6 — 1~인지지원등급 — there is no light state at all, so rho = 0 and the whole inflow is direct, by construction rather than by assumption.

prog_rate_cap = 1.0 std is a guard rather than an assumption: it caps rho at a certainty, no source bounds it because no source gives a progression rate at all, and it does not bind on any shipped model point.

Step 5 — below 65 there is no prevalence data at all. The 인정률 series is published for the 65-and-over population only, and the statute admits an under-65 applicant only through the closed list of 25 노인성 질병 — four dementia codes, one Alzheimer code, fourteen cerebrovascular codes, four Parkinson-family codes and four others, with no cancer, no musculoskeletal condition and no frailty category on the list REG-R55 별표 1 R2. So the under-65 exposure is both small and violently concentrated: of the 58,271 applicants under 65 in 2024, 뇌혈관질환군 were 49.1% and 치매질환군 26.8% R4 표2-3, derived. The two entry rates are carried down from their age-65 values on the log-gradient of the one disclosed Korean long-term-care incidence rate:

sub65_factor_at(x) = exp( −sub65_gradient × (65 − x) )   for x < 65, else 1   [std]
sub65_gradient     = ln( i(60) / i(40) ) / 20     on the combined 1·2등급 rate [S1]

which is 0.12221178 for men (13.00% a year) and 0.16479184 for women (17.91%). It carries the sex ratio with it, so a curve built on it crosses one in the late sixties, exactly where the population data finds the crossover. rho is not scaled below 65: it is a property of a life already certified, not of the gate.

The disclosed basis, and the calibration gap this model publishes rather than hides. Exactly one retrieved document gives a Korean long-term-care incidence rate — the 우체국 상품요약서’s 예정위험률 for the 1종(일반가입) form [S1]:

위험률

성

40세

50세

60세

요양(1등급) 발생률

남

0.000028

0.000080

0.000237

여

0.000010

0.000046

0.000209

요양(2등급) 발생률

남

0.000018

0.000072

0.000293

여

0.000007

0.000042

0.000250

Summing the two rows for a combined 1·2등급 rate is an upper bound, the two events being mutually exclusive at first certification, and the log-linear graduation between the three quoted ages is std. disclosed_inc_ratio_at(x) publishes the model’s own first-entry rate — direct entry plus progression by lives already certified at a light grade — over that disclosed rate. Both terms are read on the sub-65 convention the projection itself uses, the whole basis being evaluated at x_e = max(x, 65) and carried down on sub65_factor_at:

model_rate(x) = i_D(x) + P_L(x_e) rho(x_e) sub65_factor_at(x) / ( 1 − P_C(x_e) )

Reading P_L and rho at x itself below 65 — the shorter form the identity suggests — mixes an unscaled light-grade prevalence with a scaled direct rate and returns 0.2670 at 만나이 40 instead of the 0.2399 below. On the male anchor cell it runs 0.2399 at 40, 0.2465 at 50 and 0.2399 at 60: the disclosed pricing rate is about 4.2 times the model’s best estimate, almost flat in age, rising to 0.58 at 85.

Four things all point the same way and none is quantified by any retrieved source. A 예정위험률 is a loaded pricing rate for a select, underwritten, 180-day-waited population, not a best estimate. The conversion reads a cross-section as a cohort path in a scheme whose certified stock grew 71.8% in six years R4 R16, which understates entry. The care compartment is treated as leaving only by death, when 9.2% of certifications arose from a 등급변경신청 R4 표2-5, which understates entry again. And the card is quoted on 보험나이, about half a year older than this model’s 만나이. This is the largest single uncertainty in the model and it is carried as a stated sensitivity rather than closed with an invented factor.

The bracket behind care_mort_mult is the same arithmetic. In a stationary population prevalence = incidence × mean duration. R11’s 516.2 days used as the duration gives I(65+) ≈ 10.85% / 1.414 = 7.67% a year — transparently impossible, and its own refutation. The yearbook’s application-route bucket gives E ≈ 318,992 / 1.4 ≈ 228,000 first entries a year and hence D ≈ 1,165,030 / 228,000 ≈ 5.1 years [derived]; the stock roll-forward (1,097,913 → 1,165,030, a net +67,117 R18) agrees. D is near 4 to 5.5 years and the all-grade 65+ entry rate near 2 to 3.5% a year — a factor-of-two bracket, and the honest width of what the retrieved evidence supports.

Monthly conversions std. Decrements are converted geometrically, 1 − (1 − annual)^(1/12); incidence and progression are converted uniformly, annual / 12, within the policy year. The two conventions differ and the reason is that a decrement compounds against survivorship while an entry rate is applied to a stock that the same month’s decrements have not yet touched.

The dementia rider’s own basis std. A logistic (0.8298, 0.08706045, 100.12641335) fitted to the five sourced band prevalences of the 2023 치매역학조사 — 4.99% at 65–69, 5.03% at 70–74, 10.70% at 75–79, 15.57% at 80–84 and 21.18% at 85+ R7 — times the sourced 65+ sex factors, 0.9568 (M) and 1.0346 (F) R7, derived, and run through the same prevalence-to-incidence identity with the dementia state’s own excess mortality (dem_mort_mult = 2.5 std, between the light and care multiples). Every dementia case is CDR 1 or above by definition, CDR 0.5 being 경도인지장애 and not dementia, so this is the prevalence the composite’s 경도이상 tier is exposed to; a benefit at CDR 3 이상 would reach about a third of it — 경증치매 (CDR 1–2) is 67% of all dementia cases R8, and the market prices the three tiers at 3.05 : 2.06 : 1.00 [S2, derived], which agrees.

Two weaknesses of that fit are named rather than smoothed. The 65–69 and 70–74 anchors are almost equal (4.99% and 5.03%), which no logistic can reproduce, and the fit is out by 31% at 70–74. And the sex factor is applied flat in age std while the sourced series has the male rate above the female at 65–79 and below it at 80 and over R7 — so the model does not reproduce the market fact that 치매 covers are priced cheaper for women while 장기요양 covers are priced dearer (경도이상치매 여 40 ₩13,920 against 남 ₩17,400, a ratio of 0.80, in the same document that prices the main contract at 1.52 the other way) [S2, derived]. A user who turns the rider on should know that the two modules share a sex basis they should not.

dementia_wait_mths = 15 is sourced arithmetic, not a standardization: the one-year 보장개시일 [S2] [S4] plus the 90-day persistence test written into the definition of the state itself — 「진단일부터 90일 이상 계속되어 장래에 더 이상의 호전을 기대할 수 없는」 [S2]. The one-year wait is not a carrier choice: it is the settled market answer to the 2019 supervisory intervention that followed the 경증치매 boom R8 R10.

Lapse std, on a form the regulator prescribes rather than the market observes. 감독규정 제7-66조제4항 permits the 미지급형 form only where the premium was calculated using a 최적해지율 REG-R19, and the FSS’s November 2024 계리가정 ruling then fixes the shape: among models converging to zero lapse at 완납 the 로그-선형 모형 is the 원칙모형, converging to 0.1%, with a post-완납 ultimate of 0.8%; anything else is permitted only against disclosure in the audit report and the 경영공시, external actuarial verification, quarterly reporting of the difference to the FSS in CSM, best-estimate liability, K-ICS ratio and net income, and submission to an on-site inspection REG-R27. So lapse_table.csv carries three segments and a comparison vector, not a policy-year grid:

parameter

lapse_year1

lapse_completion

lapse_ultimate

lapse_level_std

annual rate

8.0%

0.1%

0.8%

4.0%

 
lapse_rate(t) = r0 × (r1 / r0)^((y − 1)/(n_Y − 1))  for policy year y ≤ n_Y     [REG-R27]
              = r2                                   for y > n_Y
lapse_rate_mth(t) = 1 − (1 − lapse_rate(t))^(1/12)                                  [std]

on the mujihae form, and lapse_level_std at every duration on the pyojun comparison vector — which is the comparison the guidance requires an insurer to disclose. Two of the four are standardizations — the 8.0% first-year level and the 4.0% 표준형 comparison level, both std — while the 0.1% and the 0.8% are the ruling’s own numbers. It has no observed range, because no Korean durational persistency series for a 보장성보험 was retrieved. The instrument-level caveat is real: the 「IFRS17 주요 계리가정 가이드라인」 attachment was never converted from HWP, so the values are verified from the 보도자료 and the functional form is unverified at instrument level REG-R27 R14, secondary.

Note what the vector says about a contract with no soft landing: with no surrender value there is no policy loan and therefore no 보험료 자동대출납입, so a missed premium lapses the contract outright REG-R25 제33조 REG-R28 — and the assumption nonetheless has lapse falling toward 납입완료. That is the regulator’s judgement, not the model’s, and it is applied here as given.

Lapse applies to the premium-paying compartments only, and that is a constraint rather than an assumption. A life in the care state has the premium waived [S3] and is barred from surrendering [S1], so pols_care is not exposed. A light-grade life is exposed on the same rate as a healthy life, because the contract does nothing for it.

Expenses and commission (all levels std; neither of the two largest is free). No 사업방법서 and no 보험료 및 해약환급금 산출방법서 was retrieved for any Korean long-term-care product, so every expense assumption here is a standardization — but the acquisition scale is bounded from above by regulation and the maintenance scale is calibrated to a sourced identity.

Input

Value

Basis

Acquisition expense

expense_acq_mths = 5.2 × P = ₩29,120 at t = 0

std, constrained: 13.0 − 7.8

Initial commission

comm_init_mths = 7.8 × P = ₩43,680 at t = 0

Sourced bound REG-R29 REG-R22: 60% of the 표준해약공제액

Renewal commission

3.0% of premium income from t = 12

std; no Korean renewal-commission scale was retrieved

Maintenance expense

₩200 per policy per month, inflating 2.0% p.a. at each 계약해당일

std, calibrated — see below

Claim expense

₩30,000 per claim event

std

Expense inflation

2.0% p.a. flat

std, the Bank of Korea target

표준해약공제액

surr_chg_ratio = 13.0 × P, running off straight-line over surr_chg_years = 7

REG-R29; REG-R19 제7-66조제1항

The acquisition expense and the initial commission together are 13 times the monthly premium, exactly the 표준해약공제액 of a 보장성보험 in the supervisor’s own rule of thumb REG-R29, split 5.2 : 7.8 so that the commission sits at the 60% cap the same release sets and 감독규정 제4-32조제8항 now carries REG-R22, and bounded from above by [별표 14] REG-R20. expense_maint is then set so that the present value of the whole expense and commission basis at the 예정이율 lands on the 20.68% loading net_prem_ratio() implies from the published 환급률 progression; it lands at 20.26%. So the expense basis is calibrated to the same two sourced facts as the account rather than picked.

The rule of thumb is used in place of the [별표 14] formula deliberately. [별표 14] states the 표준해약공제액 as 연납순보험료 × 5% × 해약공제계수 + 보험가입금액 × 10/1000 REG-R20, and the second term needs a 보험가입금액 that a product with no death benefit does not have. The chassis solves that through [별표 15] 제9호’s ratio-of-risk-premiums construction and a notional_sa_ratio std. That route is not available here: 제9호’s third bullet excludes 「치매 또는 일상생활장해 등 타인의 간병을 필요로 하는 상태」 risk premium from the very ratio REG-R21. Read literally, the formula excludes long-term-care risk premium from the notional 보험가입금액 of a long-term-care contract. The 13-month rule of thumb is the honest way through, and this document says so rather than inheriting a construction that does not apply.

The claim expense is charged per event, not per instalment. The events are the first certification, each annual 간병연금 survival test, and a dementia diagnosis. The annual — not monthly — unit is contractual: 「매년 진단 확정일에 피보험자의 주민등록등본을 제출하여야 합니다」 [S1]. The level is higher than a cancer chassis’s would be because the evidence is a 장기요양인정서 produced by a public body the insurer neither funds nor influences, and because the refusal grounds are administrative — 「허위 또는 부당 판정사실 이 확인되는 경우」 nothing is paid [S1] [S2].

The 계약자적립액 reconstruction, and why it is derived rather than assumed. av_pp(t) has two branches meeting at 납입완료. Up to it, the accumulation of the net premium at the 예정이율; after it, a sourced run-off. The run-off anchors are one carrier’s published 해약환급금 미지급형 환급률 progression at 40세, 주계약 1,000만원, 90세만기, 20년납, 월납 — 48.7% at 20 years, 54.4% at 30, 50.5% at 40, 0.0% at 50 [S2] — doubled, because that form pays 50% of the notional 기본형 value once the premiums are paid and the 해약공제 has expired. Indexing them on the fraction of the way from 납입완료 to maturity rather than on the policy year is std and is what lets one published progression serve every term and paying period. Then

net_prem_ratio() = av_ratio_at(0) × n_P / prem_accum_factor(n_P)

is the fraction of the office premium that, accumulated at the 예정이율 over the paying period, reproduces the sourced account at 납입완료 — 0.7931662309087683 on the anchor cell, implying a 예정사업비 loading of 20.68%. Deriving it is what makes the surrender-value cliff reproduce the carrier’s own figures instead of merely resembling them, and check_av_continuity() fails the moment someone replaces the derivation with a round number.

Two reconstruction steps are std and are named rather than buried. The published progression is the 미지급형’s 환급률 against its own premiums, and the model reads the doubled figure as that contract’s own 계약자적립액 — but the 기본형 comparator is a product that cannot be bought, 「’기본형’은 … 가입이 불가능하며 … 해지율을 적용하지 않고 계산합니다」 [S2], and its premium is higher, so the two accounts are not in fact the same quantity. And the run-off between the four anchors is linear, where the real curve bends with the risk cost.

Cash flow components and recursions#

Notation#

Symbol

Cells

Meaning

t

—

policy month, 0-based: t = 0, 1, …, n − 1 where n = proj_len()

n

proj_len

the number of projected months, the frame’s exclusive end; the last index is n − 1 and the maturity month is t = n − 1

x, age(t)

issue_age, age

만나이 at the 계약일; attained 만나이 x + floor(t/12)

y(t)

policy_year

policy year, the derived 1-based label floor(t/12) + 1

n_Y, n_P

prem_period_years, prem_period_mths

납입기간 in years and in months, n_P = 12 n_Y. n is the length of the projection frame — the horizon is n − 1 months — and never the paying period

P

premium_mth_pp

level monthly office premium, uw_loading × premium

A_B

lump_amount

장기요양진단급여금 sum insured

A_1, A_2

annuity_high, annuity_low

간병연금 monthly amount at 1등급 / other grades in the gate

G_B

benefit_grade

the contractual 등급 threshold

n_A, g_A

annuity_max_mths, annuity_guar_mths

120-month cap; 12-month guarantee

W, G

wait_mths, red_mths

보장개시일 and 감액기간, in whole months

P(x)

prev_rate_at

all-grade certification prevalence

s_G(x)

share_ge_at

share of certified lives at grade G or above

P_C(x), P_L(x)

prev_care_at, prev_light_at

prevalence at/above and below G_B

mu_H, mu_L, mu_C, mu_bar

mort_force_*_at

the four forces of mortality

i_D, i_L, rho

inc_rate_direct_at, inc_rate_light_at, prog_rate_at

the three annual transition rates; _mth = /12

q_H(t), q_L(t), q_C(t)

mort_rate_*_mth

monthly mortality of the three compartments

w(t)

lapse_rate_mth

monthly lapse, on the paying compartments only

h, l_L, l_C, l

pols_healthy, pols_light, pols_care, pols_if

the three compartments and their total

n_L, n_D, n_P*, n_C

pols_entry_light, pols_entry_care_direct, pols_entry_care_prog, pols_entry_care

the month’s certifications

r(t)

red_factor

감액 factor applying to a certification dated in month t

A(s)

ann_amount_at

the frozen monthly annuity of the cohort certified in month s

S_C(s, t)

care_surv

care-state survival from month s to month t

AV(t), CV(t)

av_pp, cv_pp

계약자적립액; 해약환급금

CF(t)

net_cf

net cash flow, income-positive

Dimensional check. P, P_C, P_L and s_G are dimensionless proportions of a population; P', P_C', i_D, i_L and rho are rates per year; mu_H, mu_L, mu_C, mu_bar are forces per year; q_*, w are probabilities per month. prev_beta carries units of 1/year, which is why P' = beta P (1 − P/ceil) comes out as a rate per year and can be added to P_C (mu_C − mu_bar), also a rate per year — the two terms of the identity are dimensionally the same object, and a version that adds a prevalence to a rate is the commonest way to get this wrong. A_B is KRW per event, A_1 and A_2 KRW per instalment, so A_B r(t) n_C(t) and A(s) n_C(s) S_C(·) are KRW per policy-month. The error this check catches is the one that dominates this product: multiplying the published 인정률 — a prevalence, 10.85% at 65+ — by a benefit amount as if it were an annual claim frequency.

The four-compartment chain and its processing order#

For t = 0, 1, …, n − 2 — the months of cover; the terminal month t = n − 1 is the maturity row and carries no cash flow — with the state at the start of the month being h(t), l_L(t), l_C(t):

1. Start of month — premium, maintenance expense, renewal commission.

premiums(t)    = P × pols_act(t)              for t < n_P,  else 0
expenses(t)    = expense_acq_mths × P × 1{t = 0}
                 + expense_maint × (1 + pi)^floor(t/12) × pols_if(t)
commissions(t) = comm_init_mths × P × 1{t = 0} + 0.03 × premiums(t) × 1{t ≥ 12}

Premium rides on pols_act, never on pols_if: the 납입면제 waives the 기본계약 and every attached rider from the award of 1·2등급 [S3], and waived premiums are treated as paid. Maintenance expense rides on pols_if, including lives on waiver — the policy is still administered when nobody is paying for it.

2. Certification, from the start-of-month counts.

n_L(t) = h(t)   × i_L(age(t))  / 12
n_D(t) = h(t)   × i_D(age(t))  / 12
n_P*(t)= l_L(t) × rho(age(t))  / 12

n_C(t)   = n_D(t) + n_P*(t)   for t ≥ W ;  0 otherwise
void(t)  = n_D(t) + n_P*(t)   for t < W ;  0 otherwise

n_L is drawn from the never-certified population alone. n_P* — progression — is drawn from the light compartment, and above 65 it is the dominant route. Inside the 보장개시일 window a certification does not defer the claim: the benefit is 무효, the premiums paid for it come back, and the life leaves the model. void is therefore a decrement, not a claim refusal, and the two are kept apart because the 약관 keep them apart.

3. End of month — benefits and the claim-handling expense.

claims_lump(t)     = A_B × r(t) × n_C(t)
claims_annuity(t)  = ann_pay(t)
claims_dementia(t) = dementia_amount × pols_entry_dem(t)
claims_death(t)    = AV(t) × pols_death_act(t)
claims_lapse(t)    = CV(t) × pols_lapse(t)
claims_void(t)     = cum_prem_pp(t + 1) × void(t)
claims_maturity(t) = 0
claim_expenses(t)  = expense_claim × ( n_C(t) + ann_tests(t) + pols_entry_dem(t) )

4. Mortality, on the mid-month counts.

h_mid(t)   = h(t)   − n_L(t) − n_D(t)
l_L_mid(t) = l_L(t) + n_L(t) − n_P*(t)
l_C_mid(t) = l_C(t) + n_C(t)                     — the voided are NOT here

pols_death_act(t)  = h_mid(t) q_H(t) + l_L_mid(t) q_L(t)
pols_death_care(t) = l_C_mid(t) q_C(t)

Only pols_death_act pays: deaths in the care state pay nothing, 「지급사유가 발생한 후 사망한 경우에는 별도로 책임준비금을 지급하지 않습니다」 [S1]. That split is a cash-flow distinction and not bookkeeping.

5. Lapse, on the mortality survivors of the paying compartments only.

pols_lapse(t) = ( h_mid(t) (1 − q_H(t)) + l_L_mid(t) (1 − q_L(t)) ) × w(t)

6. Roll forward.

h(t+1)   = h_mid(t)   × (1 − q_H(t)) × (1 − w(t))
l_L(t+1) = l_L_mid(t) × (1 − q_L(t)) × (1 − w(t))
l_C(t+1) = l_C_mid(t) × (1 − q_C(t))
l(t+1)   = h(t+1) + l_L(t+1) + l_C(t+1)

7. Maturity on the frame’s last row t = n − 1: pols_maturity(n − 1) = pols_if(n − 1), paying nothing.

check_pols_roll_fwd() asserts, over t = 0 … n − 1,

l(t) − l(t+1) = pols_death(t) + pols_lapse(t) + void(t) + pols_maturity(t)

with a tolerance of roll_fwd_tol = 1e-12, and check_nesting() asserts that the three compartments are non-negative, add to pols_if, and contain the dementia counter.

The 감액 factor, and the fact that it is frozen#

r(t) = 1 − (1 − red_fraction) × disease_share     for t < G
     = 1                                          for t ≥ G

with red_fraction = 0.50 sourced [S4] and invariant wherever a 감액 is stated. The 약관 test is on the cause, not on the grade: a 질병-caused certification inside the window is paid at 50%, an 상해/재해-caused one in full [S4]. The relative frequency of the two is given by no retrieved source, so disease_share = 0.95 is std and the accident carve-out is named rather than dropped; the blended factor is 0.525.

r is evaluated at the certification month s, never at the payment month. 「최초 진단 확정일을 기준으로 경과기간 2년미만의 보험금 감액여부가 결정됩니다. 따라서 … 그 이후에 도래하는 매년 진단 확정일이 계약일부터 2년이상에 해당하더라도 … 지급액은 변경되지 않습니다」 [S1]. A claim that starts inside the reduction window stays halved for the whole ten years of the annuity.

The 간병연금 ledger#

The cohort certified in month s is paid monthly in months s … s + n_A − 1. The first g_A instalments are guaranteed against death; each later block of twelve is released only by the annual survival test on the anniversary of the 진단확정일:

S_C(s, t)      = product over u = s … t−1 of ( 1 − q_C(u) )
weight(u)      = 1                                for u < g_A
               = S_C(s, s + 12 × floor(u/12))     otherwise
ann_count(t)   = sum over u = 0 … min(t, n_A − 1) of  n_C(t − u) × weight(u)
ann_pay(t)     = sum over the same u of  A(t − u) × n_C(t − u) × weight(u)
ann_tests(t)   = sum over k = 1 … n_A/12 − 1 of  n_C(t − 12k) × S_C(t − 12k, t)

with the frozen amount

A(s) = [ s_1(x_s) A_1 + ( s_G(x_s) − s_1(x_s) ) A_2 ] / s_G(x_s)  ×  r(s)
x_s  = max( age(s), 65 )

— the age-specific grade blend of A_1 at 1등급 and A_2 at every other grade inside the gate, times the 감액 factor at s. Both the amount and the reduction are frozen at s, which is what makes a cohort entering at 만나이 68 keep its own amount for all ten years whatever later cohorts are paid.

Three properties of this ledger deserve to be in front of a reader.

  • The u = 0 term is n_C(t) itself. The first instalment falls in the month of certification, not a year later [S1]. Deferring it removes roughly a tenth of the annuity liability and misdates all of it.

  • S_C is computed as a partial product, never as a ratio of cumulative products. q_C is min(1, 3 q(x)) and the cap binds from 만나이 108 on the shipped male table — 3 × q(108) = 1.0714 — and from 112 on the female one, so a cumulative product underflows to zero from there on and the ratio form divides by zero exactly where the tail of a 종신 variant of this liability would live.

  • The cap and the maturity truncation bind jointly. Nothing is paid on the maturity row t = n − 1 or after it, so a life certified at 만나이 85 on a 90세만기 contract gets five years of annuity and not ten. That is the conservative reading of a question no retrieved document resolves std, and it materially understates the benefit for a late entrant.

check_ann_ledger() rebuilds ann_count(t) by scanning every month in the window t − n_A < s ≤ t and re-deriving each cohort’s weight from its own age, rather than stepping back through the same loop. A ledger that paid the first instalment a year late, that ran past the cap, that lost the twelve-month guarantee, or that used a ratio form of S_C, shows up there.

The 계약자적립액 and the 해약환급금#

cum_prem_pp(t)      = P × min(t, n_P)          — paid before month t's own premium
prem_accum_factor(t)= (1 + j) ( (1 + j)^t − 1 ) / j,   j = (1 + 0.02)^(1/12) − 1
net_prem_ratio()    = av_ratio_at(0) × n_P / prem_accum_factor(n_P)

AV(t) = net_prem_ratio() × P × prem_accum_factor(t)             for t ≤ n_P
      = av_ratio_at( (t − n_P) / (n − 1 − n_P) ) × P × n_P      for t > n_P

surr_chg_pp(t) = surr_chg_ratio × P × ( 1 − t / n_chg ),  n_chg = 12 min(7, n_Y)
               = 0 for t ≥ n_chg

CV(t) | mijigeup     = 0                for t < n_P ;  0.5 × AV(t) otherwise
      | half_during  = 0.5 × AV(t)      for t < n_P ;  AV(t)       otherwise
      | pyojun       = max( AV(t) − surr_chg_pp(t), 0 )

Reading 「50%」 without reading which side of 납입완료 it attaches to puts the cliff upside down, which is why the form is a model point field and not a switch on a ratio. Four forms are on the Korean shelf under three nearly identical names and they are different products, not variants: 미지급형 pays nothing during and 50% of a notional 기본형 after [S2]; 납입중50%해약환급금지급형 pays 50% during and 100% after [S4]; 삼성화재 sells the pure protection form with 「만기환급금 : 없음」 and no 무·저해지 variant in the retrieved extract [S3]; and 우체국 is a conventional 표준형 with a normal surrender value from year 1, because 우정사업본부 business is not written under 보험업법 [S1]. check_cv_form() asserts the sign of the cliff, not merely its magnitude.

Net cash flow#

net_cf(t) = premiums(t)
          − claims_lump(t) − claims_annuity(t) − claims_dementia(t)
          − claims_death(t) − claims_lapse(t)  − claims_void(t)
          − claims_maturity(t)
          − expenses(t) − claim_expenses(t) − commissions(t)

net_cf is income-positive, which is this library’s sign and this document’s own, so there is deliberately no outgo-positive liability_cf companion to publish and the conventions suite skips its orientation test on that basis. check_net_cf() asserts that net_cf re-adds from exactly the eleven published columns of result_cf(), to val_tol = 1e-06: the house contract is that no model’s headline number is reconciled only in prose.

Note that claims_death is not a death benefit. The contract has none. It is the 계약자적립액 that 감독규정 제7-63조제1항제1호 makes payable on a death from a cause the contract does not cover REG-R17, and on the anchor cell it is ₩326,783.93 undiscounted against ₩973,533.06 of premium — a third of premium income — because 35.4% of the cohort dies before maturity and the account is worth close to cumulative premiums at long durations. That is a genuine and distinctive Korean result and it should be read, not smoothed. The Japanese counterpart has no such payment at all.

Optional modules (all off in the base run except the 간병연금)#

Module

Switch

Base run

간병연금

annuity_on

On. It is two thirds of the anchor cell’s benefit outgo and the reason the product is a three-state model

치매진단급여금

dementia_rider, dementia_amount

Off. A different trigger (CDR, a 치매 전문의) with a different sex basis and a 15-month effective wait

간편심사

uw_loading

Off (1.0). A premium multiplier only: no retrieved source gives the simplified pool’s incidence, so on a loaded point the extra premium is pure margin in this model

Threshold

benefit_grade

g2. g1 … g6 reachable without a second chassis

Surrender-value form

cv_form

mijigeup. half_during and pyojun as switches

Lapse vector

lapse_form

mujihae. pyojun is the level comparison vector REG-R27 requires an insurer to disclose

Waiting / reduction

wait_mths, red_mths

3 / 12. The 우체국 6 / 24 combination is model point 9

Not modelled, and each is a deliberate scope decision. The utilisation-conditioned 지원금 riders [S2] — which pay ₩100,000 a month only where the insured is actually using 재가급여, 시설급여, 주·야간보호 or 복지용구 — need a utilisation rate by grade, by service type and by duration since certification, which no retrieved source gives; R4 표3-3 gives 급여이용 수급자 by service type as a national aggregate with substantial overlap, not the cross-tabulation the module would need, and a module whose central assumption would be entirely std adds nothing. The 종신 income form [S2] [S5] carries the whole longevity tail after onset with no cap on a post-onset mortality basis nobody publishes. The 두 번째 장기요양지원금(1~2등급) persistency rider, with its five-year 면책 running from the first 1·2등급 판정일 [S3], needs exactly the continuance basis that does not exist. The 간병인사용일당 is a different product. And 교보’s premium refund on a 1~4등급 진단 [S5] would materially change the reserve; it is a press-release fact whose mechanics are unverified.

Policyholder behavior modeling#

  • Lapse stops at the benefit trigger, and here that is a constraint, not a refinement. Once 1·2등급 is awarded the premium is waived [S3] and the 약관 bars surrender outright — 「최초 지급사유가 발생한 후에는 이 특약을 해지할 수 없습니다」 [S1] — so zero lapse in the care state is what the contract says. Applying lapse there is not a conservative choice; it is a wrong one, and it is silent: the annuity ledger is driven by n_C and S_C, not by pols_care, so the annuity does not move at all and the only visible effect is a surrender value paid to a life that cannot surrender. See the pitfalls.

  • The waiver fires on the same event as the benefit, which inverts the Japanese pattern. In jplib’s 介護保険 the waiver fires at a lower grade than the lump sum and creates a band of lives paying nothing and claiming nothing — the single most mis-modelled item in that product. Here G_W = G_B, following the only observed whole-contract waiver [S3], so there is no such band. But the waiver is not free: it stops the premium for as long as the insured survives in the care state, which is exactly the quantity the prevalence-to-incidence conversion cannot pin down. The waiver is where post-onset mortality enters even a lump-sum-only version of this contract. On the anchor cell it costs ₩414.65 of premium income over the paying period, 0.043% of the total — small only because the certification rate at issue age 40 is small.

  • The light compartment pays and lapses, and that is the delta against the Japanese product and the parallel with the chassis. A 3~5등급 life has been certified by the state, carries impaired mortality, and receives nothing; the contract goes on charging it and it can still walk away. Over the anchor cell’s projection the light compartment accumulates 10.79 policy-months of exposure against the care compartment’s 1.74.

  • Anti-selection is at the front door, and it is unusually direct. What is being selected against is an application to a public body that leaves a record, which is why the 간편심사 question set asks 「현재 노인장기요양보험에 의한 장기요양급여 수급자이거나 장기요양인정 심의 중입니까?」 [S2] and why one carrier will not attach its 장기요양 riders to a simplified chassis at all — 「주계약 1종(일반가입)에 한하여 부가 가능」 [S1]. That refusal is itself a statement about anti-selection on this trigger. The composite is fully underwritten; no selection loading is applied at issue, and the 간편심사 pool is carried as a premium multiplier with its incidence unchanged, so the true claim cost of that pool is understated in this model.

  • The waiting period is anti-selection with teeth. A certification inside the window does not merely fail: the benefit is 무효 and premiums come back [S1] [S2]. Unlike the chassis there is no cancellation option and no revival, so an insured certified during the window has bought a benefit that can never pay for that certification. And reinstatement is not a rewind: every waiting period in the file is measured 「계약일[부활(효력회복)일]부터」 [S1] [S2], so a reinstated contract serves its 90 days again from the 부활일. krlib treats 부활 as a new model point, not as a negative lapse, and the base run treats lapse as absorbing [std scope].

  • Thresholds and amounts are elected at issue and cannot move. benefit_grade, lump_amount, annuity_high and annuity_low are model-point attributes. A code path that varies them over t models a contract term that does not exist.

  • 청약철회 is out of scope. A 15-day withdrawal right under 금융소비자보호법 제46조 as implemented in 표준약관 제17조 REG-R25 REG-R51; krlib models from the point cover is in force and has no new-business funnel in which to represent it.

  • The claimant usually cannot claim. A 지정대리청구인 is designated on every retrieved product [S1] [S3]. It has no cash-flow effect in this model and it is the operational fact that most distinguishes administering this product from administering the chassis.

Worked example#

Anchor cell (point_id = 1, policy_id = LTC-000001). Male, 만나이 40 at the 계약일, 90세만기, 20년납, 월납, 해약환급금 미지급형, 일반심사. 장기요양(1~2등급) 진단급여금 A_B = ₩10,000,000; 간병연금 on at A_1 = ₩500,000 / A_2 = ₩300,000 a month with a 12-month guarantee and a 120-month cap; 치매 rider off; 보장개시일 W = 3 months; 감액기간 G = 12 months; lapse_form = mujihae; office premium P = ₩5,600 a month. proj_len() = 12 × (90 − 40) + 1 = 601, so result_cf() carries 601 rows, indexed t = 0 … 600.

Every assumption value the first rows use#

All at 만나이 40 and in policy year 1, so one set of rates drives rows t = 0 … 11.

Quantity

Value

Basis

mort_rate(0) = q(40)

0.00097601273

std Makeham–Gompertz on the 경험생명표 65세 기대여명 anchor REG-R33 REG-R34

mort_rate_mth(0) = q_H

0.0000813708009308467

1 − (1 − q)^(1/12) std

mort_rate_light(0)

0.001756822914

1.8 × q std

mort_rate_light_mth(0) = q_L

0.0001465199263399608

std

mort_rate_care(0)

0.00292803819

3.0 × q std

mort_rate_care_mth(0) = q_C

0.00024433125292278035

std

lapse_rate(0)

0.08

std first-year level; shape REG-R27

lapse_rate_mth(0) = w

0.006924382628299419

std

P(40)

0.00038039917723430234

fitted logistic std through R4

P_C(40)

0.00008444861734601512

s_g2(40) × P(40), s_g2(40) = 0.222 R4, derived

P_L(40)

0.0002959505598882872

P − P_C

sub65_factor_at(40)

0.04710884458012182

exp(−0.12221178 × 25), the [S1] gradient

i_D(40)

0.0000022292964462128687

direct entry, per year

i_L(40)

0.00010426974412244515

light-grade entry, per year

rho(40)

0.03396845379835368

progression, per year — not scaled below 65

i_D(40)/12

0.00000018577470385107238

monthly std

i_L(40)/12

0.000008689145343537096

monthly std

rho(40)/12

0.0028307044831961396

monthly std

disclosed_inc_at(40)

0.000046

[S1], 요양 1등급 + 2등급 발생률 at 40세 남

disclosed_inc_ratio_at(40)

0.23993880644434135

the model’s own first-entry rate over it

red_factor(t), t < 12

0.525

1 − 0.5 × 0.95; red_fraction [S4], disease_share std

red_factor(t), t ≥ 12

1.0

[S4]

ann_amount_at(s), s < 12

207495.7410562181

grade blend at 만나이 65 × 0.525

ann_amount_at(s), 12 ≤ s, 만나이 ≤ 65

395229.98296422494

grade blend at 만나이 65

expense_acq_mths × P

29120.0

5.2 months std, constrained by REG-R29

expense_maint

200.0

std, calibrated to net_prem_ratio()

comm_init_pp()

43680.0

7.8 months, the 60% cap REG-R29 REG-R22

expense_claim

30000.0

per event std

net_prem_ratio()

0.7931662309087683

derived from av_ratio_at(0) = 0.974 [S2]

Every decrement above is a construction. None is an insurer’s basis and none could be: the 산출방법서 is a 기초서류 and is not public REG-R2, 경험생명표 is not published in full REG-R33 REG-R34, and 보험개발원 publishes neither a 장기요양 incidence table nor a post-onset mortality table. The only retrieved Korean long-term-care rate anywhere is one carrier’s 예정위험률 [S1], and this model uses it for its gradient and sex ratio, never for its level.

The first policy year, cash flow#

Values as the model produces them, to six decimal places. claims_dementia, claims_lapse and claims_maturity are identically zero over this range and are omitted; they are in the totals below.

t

pols_if

premiums

claims_lump

claims_annuity

claims_death

claims_void

expenses

claim_expenses

commissions

net_cf

0

1.000000

5600.000000

0.000000

0.000000

0.000000

0.001040

29320.000000

0.000000

43680.000000

-67400.001040

1

0.992995

5560.769900

0.000000

0.000000

0.359493

0.002340

198.598925

0.000000

0.000000

5361.809142

2

0.986038

5521.814482

0.000000

0.000000

0.714544

0.003891

197.207660

0.000000

0.000000

5323.888388

3

0.979131

5483.131826

1.333122

0.052689

1.065193

0.000000

195.826137

0.007618

0.000000

5284.847067

4

0.972272

5444.720021

1.448226

0.109927

1.411483

0.000000

194.454337

0.008276

0.000000

5247.287772

5

0.965461

5406.577174

1.561294

0.171634

1.753454

0.000000

193.092148

0.008922

0.000000

5209.989723

6

0.958698

5368.701402

1.672351

0.237731

2.091145

0.000000

191.739501

0.009556

0.000000

5172.951118

7

0.951982

5331.090836

1.781423

0.308138

2.424598

0.000000

190.396330

0.010180

0.000000

5136.170167

8

0.945313

5293.743621

1.888537

0.382778

2.753852

0.000000

189.062569

0.010792

0.000000

5099.645094

9

0.938691

5256.657915

1.993717

0.461576

3.078946

0.000000

187.738151

0.011393

0.000000

5063.374132

10

0.932115

5219.831887

2.096990

0.544455

3.399919

0.000000

186.423012

0.011983

0.000000

5027.355528

11

0.925585

5183.263720

2.198380

0.631342

3.716809

0.000000

185.117086

0.012562

0.000000

4991.587540

12

0.919102

5146.951609

4.601130

0.813192

4.308813

0.000000

187.496714

0.013803

154.408548

4795.309407

Four rows in that table are where the product does something.

  • t = 0 is the new-business strain: one month’s premium against 5.2 months of acquisition expense, one month of maintenance and the whole 7.8 months of initial commission — and, because of the row below, ₩0.001040 of refund on top.

  • t = 0, t = 1 and t = 2 carry a non-zero claims_void and no other benefit. These are the certifications inside the 보장개시일 window: the cover is 무효 and the premiums paid for it come back. The refund is cum_prem_pp(t + 1), not cum_prem_pp(t) — premium falls at the start of month t and the void is recognised at the end of it, so a life voided in month 0 has paid one month’s premium and gets it back, which is why claims_void(0) is ₩0.001040 rather than nil. Valuing the refund at cum_prem_pp(t) would leave the insurer holding a month’s premium on a cover it had just declared never to have existed.

  • t = 3 is the first payable certification: the 보장개시일 is three whole months, so claims_lump and claims_annuity both start here, and claim_expenses with them.

  • t = 12 is the 감액기간 expiring and the renewal commission starting, in the same row. claims_lump roughly doubles — from 2.198380 to 4.601130 — because red_factor steps from 0.525 to 1.0, and commissions goes from nil to 3% of premium. The expenses line also steps, from 185.117086 to 187.496714, because the 2% expense inflation factor increments at the 계약해당일 even though the in-force count has fallen.

The compartments, first policy year#

Policy counts to ten decimal places.

t

pols_healthy

pols_light

pols_care

pols_entry_light

pols_entry_care_direct

pols_entry_care_prog

pols_entry_care

pols_void

pols_death_act

pols_lapse

0

1.0000000000

0.0000000000

0.0000000000

0.0000086891

0.0000001858

0.0000000000

0.0000000000

0.0000001858

0.0000813714

0.0069238179

1

0.9929859973

0.0000086277

0.0000000000

0.0000086282

0.0000001845

0.0000000244

0.0000000000

0.0000002089

0.0000808019

0.0068753138

2

0.9860211908

0.0000171097

0.0000000000

0.0000085677

0.0000001832

0.0000000484

0.0000000000

0.0000002316

0.0000802364

0.0068271493

3

0.9791052354

0.0000254477

0.0000000000

0.0000085076

0.0000001819

0.0000000720

0.0000002539

0.0000000000

0.0000796748

0.0067793220

4

0.9722377886

0.0000336437

0.0000002539

0.0000084479

0.0000001806

0.0000000952

0.0000002759

0.0000000000

0.0000791172

0.0067318297

5

0.9654185101

0.0000416995

0.0000005296

0.0000083887

0.0000001794

0.0000001180

0.0000002974

0.0000000000

0.0000785635

0.0066846698

6

0.9586470621

0.0000496168

0.0000008268

0.0000083298

0.0000001781

0.0000001405

0.0000003185

0.0000000000

0.0000780137

0.0066378402

7

0.9519231089

0.0000573975

0.0000011450

0.0000082714

0.0000001768

0.0000001625

0.0000003393

0.0000000000

0.0000774677

0.0065913385

8

0.9452463176

0.0000650433

0.0000014840

0.0000082134

0.0000001756

0.0000001841

0.0000003597

0.0000000000

0.0000769255

0.0065451624

9

0.9386163574

0.0000725560

0.0000018433

0.0000081558

0.0000001744

0.0000002054

0.0000003798

0.0000000000

0.0000763871

0.0064993096

10

0.9320328997

0.0000799372

0.0000022225

0.0000080986

0.0000001731

0.0000002263

0.0000003994

0.0000000000

0.0000758525

0.0064537779

11

0.9254956184

0.0000871887

0.0000026213

0.0000080418

0.0000001719

0.0000002468

0.0000004187

0.0000000000

0.0000753216

0.0064085651

12

0.9190041896

0.0000943121

0.0000030393

0.0000090234

0.0000001929

0.0000002672

0.0000004601

0.0000000000

0.0000799758

0.0050125240

Two things to read out of it. pols_care(3) is still zero: the certifications of month 3 are paid in month 3 but enter the stock at the start of month 4. And pols_entry_care_prog overtakes pols_entry_care_direct between t = 7 and t = 8 — eight months into the contract, at 만나이 40, with the light compartment still only 0.0000650 of the block. Progression is the dominant route from almost the first year, which is the whole point of the four-compartment structure.

Hand traces#

Trace, month 0. h(0) = 1, l_L(0) = l_C(0) = 0, so pols_act(0) = pols_if(0) = 1.

Premium = 5,600 × 1 = 5,600.000000.

Certifications: n_L(0) = 1 × 0.000008689145343537096 = 0.0000086891; n_D(0) = 1 × 0.00000018577470385107238 = 0.0000001858; n_P*(0) = 0 × 0.0028307 = 0 — there is no light compartment to progress out of yet. Because 0 = t < W = 3, n_C(0) = 0 and void(0) = 0.0000001858 + 0 = 0.00000018577470385107238. claims_void(0) = cum_prem_pp(1) × void(0) = 5,600 × 0.00000018577470385107238 = 0.001040 — the refund is valued on the premiums paid by the end of the month, and one has been: the month-0 premium fell at the start of it.

Mid-month counts: h_mid(0) = 1 − 0.0000086891 − 0.0000001858 = 0.9999911250799526; l_L_mid(0) = 0 + 0.0000086891 − 0 = 0.000008689145343537096; l_C_mid(0) = 0.

Mortality: `pols_death_act(0) = 0.9999911250799526 × 0.0000813708009308467

  • 0.000008689145343537096 × 0.0001465199263399608 = 0.0000813713519. claims_death(0) = AV(0) × 0.0000813714 = 0 × … = 0.000000`, because the account opens at nil.

Lapse: `pols_lapse(0) = ( 0.9999911250799526 × (1 − 0.0000813708009308467)

  • 0.000008689145343537096 × (1 − 0.0001465199263399608) ) × 0.006924382628299419 = 0.0069238178955`.

Expenses: 5.2 × 5,600 = 29,120 acquisition plus 200 × 1.02^0 × 1 = 200 maintenance = 29,320.000000. Commission = 7.8 × 5,600 = 43,680.000000. Claim expense = 30,000 × (0 + 0 + 0) = 0.

net_cf(0) = 5,600.000000 − 0 − 0 − 0 − 0 − 0.001040 − 29,320.000000 − 0 − 43,680.000000 = −67,400.001040.

Roll forward: h(1) = 0.9999911250799526 × (1 − 0.0000813708009308467) × (1 − 0.006924382628299419) = 0.9929859973; l_L(1) = 0.000008689145343537096 × (1 − 0.0001465199263399608) × (1 − 0.006924382628299419) = 0.0000086277; l_C(1) = 0; pols_if(1) = 0.9929859973 + 0.0000086277 + 0 = 0.992995.

Trace, month 1. Every per-policy rate is unchanged — age(1) = 40, policy year still 1.

Premium = 5,600 × pols_act(1) = 5,600 × 0.992994624977843 = 5,560.769900. Note it rides on pols_act, which here equals pols_if only because the care compartment is still empty.

Certifications: n_L(1) = 0.9929859973 × 0.000008689145343537096 = 0.0000086282; n_D(1) = 0.9929859973 × 0.00000018577470385107238 = 0.0000001845; n_P*(1) = l_L(1) × rho/12 = 0.0000086277 × 0.0028307044831961396 = 0.0000000244 — the first progression in the model. 1 = t < W = 3, so n_C(1) = 0 and void(1) = 0.0000001845 + 0.0000000244 = 0.00000020889418843702306.

claims_void(1) = cum_prem_pp(2) × void(1) = 11,200 × 0.00000020889418843702306 = 0.002340.

The account: AV(1) = net_prem_ratio() × P × prem_accum_factor(1) = 0.7931662309087683 × 5,600 × 1.0016515813 = 4,449.066773, so claims_death(1) = 4,449.066773 × 0.0000808019 = 0.359493.

Expenses = 200 × 1.02^0 × 0.992994624977843 = 198.598925; no acquisition after t = 0, no renewal commission before t = 12, no claim expense because nothing payable happened.

net_cf(1) = 5,560.769900 − 0.359493 − 0.002340 − 198.598925 = 5,361.809142.

Trace, month 3 — the first payable certification. h(3) = 0.9791052354319798, l_L(3) = 0.0000254477, l_C(3) = 0.

n_D(3) = 0.9791052354319798 × 0.00000018577470385107238 = 0.00000018189298515141055; n_P*(3) = 0.0000254477 × 0.0028307044831961396 = 0.00000007203498063473715. Now t = 3 ≥ W = 3, so n_C(3) = 0.00000018189 + 0.00000007203 = 0.0000002539279657861477 and void(3) = 0.

The lump sum, at the reduced factor because 3 < G = 12: claims_lump(3) = 10,000,000 × 0.525 × 0.0000002539279657861477 = 1.333122.

The annuity’s first instalment falls in the same month. The frozen amount is the grade blend at x_s = max(40, 65) = 65, where s_g1(65) = 0.07985714285714286 and s_g2(65) = 0.1677142857142857:

blended = ( 0.07985714285714286 × 500,000
          + (0.1677142857142857 − 0.07985714285714286) × 300,000 ) / 0.1677142857142857
        = ( 39,928.571429 + 26,357.142857 ) / 0.1677142857142857
        = 395,229.98296422494

times red_factor(3) = 0.525 gives A(3) = 207,495.7410562181. With u = 0 and therefore weight = 1,

claims_annuity(3) = 207,495.7410562181 × 0.0000002539279657861477 = 0.052689

Claim expense = 30,000 × (0.0000002539279657861477 + 0 + 0) = 0.007618 — one event, the certification; the first annual survival test is twelve months away.

claims_death(3) = AV(3) × pols_death_act(3) = 13,369.256441 × 0.0000796748 = 1.065193. Expenses = 200 × 0.9791306831539381 = 195.826137. Premium = 5,600 × 0.9791306831539381 = 5,483.131826.

net_cf(3) = 5,483.131826 − 1.333122 − 0.052689 − 1.065193 − 195.826137 − 0.007618 = 5,284.847067.

Trace, month 12 — the 감액 expires and the renewal commission starts. age(12) = 41, policy year 2, so the rates move: lapse_rate(12) = 0.06352246697177472 on the log-linear path, and red_factor(12) = 1.0.

n_C(12) = 0.0000001929 + 0.0000002672 = 0.00000046011303806134214, so claims_lump(12) = 10,000,000 × 1.0 × 0.00000046011303806134214 = 4.601130 — a step of 4.601130 / 2.198380 = 2.09 against month 11, of which a factor of 1/0.525 = 1.90 is the 감액 expiring and the rest is the rising certification rate.

ann_pay(12) sums the cohorts certified in months 3 through 12, each at its own frozen amount and each with u = 12 − s < 12, so every weight is 1 (the guarantee): ann_pay(12) = 0.813192. The cohorts of months 3–11 are still carried at A = 207,495.7410562181; only the month-12 cohort is at 395,229.98296422494. That is the freeze doing its work, and it is the reason claims_annuity does not step at t = 12 the way claims_lump does.

Commission = 0.03 × 5,146.951609 = 154.408548. Expenses = 200 × 1.02^1 × 0.9191015410 = 187.496714. Claim expense = 30,000 × 0.00000046011303806134214 = 0.013803 — still no survival test, because the first cohort’s first anniversary is month 15.

net_cf(12) = 5,146.951609 − 4.601130 − 0.813192 − 4.308813 − 187.496714 − 0.013803 − 154.408548 = 4,795.309407.

Trace, month 240 — the surrender-value cliff. t = 240 = n_P, so the premium stops and the account crosses from its accumulation branch to its sourced run-off branch. The two meet by construction:

AV(240) = net_prem_ratio() × 5,600 × prem_accum_factor(240)
        = 0.7931662309087683 × 5,600 × 294.7175395152288 = 1,309,056.0000
        = av_ratio_at(0) × 5,600 × 240 = 0.974 × 1,344,000 = 1,309,056.0000

and check_av_continuity() asserts exactly that. The surrender value steps with it: cv_pp(239) = 0 and cv_pp(240) = 0.5 × 1,309,056 = 654,528.0000, which against cum_prem_pp(240) = 1,344,000 is a 환급률 of 48.700000%, the published figure [S2]. That is an identity, not a check: av_table.csv’s first anchor is that published 48.7%, doubled, so what reproduces here is the arithmetic joining the two branches and nothing about the basis.

Two things step at once and their product is the cliff. The lapse rate goes from lapse_rate(239) = 0.001 — the 납입완료 convergence point — to lapse_rate(240) = 0.008, the post-완납 ultimate REG-R27, so pols_lapse jumps from 0.0000536909 to 0.0004306951, a factor of eight. And the value paid on each of those lapses jumps from nil to ₩654,528. So

claims_lapse(239) = 0 × 0.0000536909            = 0.0000
claims_lapse(240) = 654,528.0 × 0.0004306951    = 281.9020

and net_cf goes from +2,496.2682 at t = 239 to −1,284.5196 at t = 240. The contract turns from a net income stream into a net outgo stream in one month, and the surrender-value form is a bigger part of that turn than the premium stopping.

Milestone rows#

To four decimal places. claims_dementia and claims_maturity are zero throughout.

t

만나이

pols_if

pols_act

pols_care

premiums

claims_lump

claims_annuity

claims_death

claims_lapse

expenses

claim_expenses

commissions

net_cf

12

41

0.9191

0.9191

0.0000

5146.9516

4.6011

0.8132

4.3088

0.0000

187.4967

0.0138

154.4085

4795.3094

120

50

0.6891

0.6889

0.0002

3857.6317

37.4014

80.2047

69.6691

0.0000

167.9928

0.5636

115.7290

3386.0712

239

59

0.6453

0.6442

0.0011

3607.7963

139.1227

361.8337

311.9062

0.0000

188.0242

2.4075

108.2339

2496.2682

240

60

0.6450

0.6439

0.0011

0.0000

101.8715

364.1340

342.5724

281.9020

191.6972

2.3426

0.0000

-1284.5196

241

60

0.6443

0.6432

0.0011

0.0000

102.8477

366.4506

342.5552

281.8690

191.4910

2.3662

0.0000

-1287.5797

300

65

0.6016

0.5999

0.0017

0.0000

124.6609

493.3706

534.0717

277.9321

197.3947

3.0831

0.0000

-1630.5131

360

70

0.5513

0.5488

0.0025

0.0000

252.6475

651.6038

826.1459

268.1912

199.7145

4.3504

0.0000

-2202.6533

480

80

0.4151

0.4096

0.0056

0.0000

771.8873

1656.5015

1546.9336

185.4590

183.3274

11.6465

0.0000

-4355.7552

540

85

0.3212

0.3128

0.0084

0.0000

1681.5930

2788.4692

1004.5705

70.6471

156.5864

20.6729

0.0000

-5722.5392

599

89

0.2120

0.2017

0.0103

0.0000

1844.5927

3756.1556

17.0540

0.7571

111.8860

24.9810

0.0000

-5755.4264

600

90

0.2102

0.1999

0.0102

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

Rows t = 299 → 300 and t = 479 → 480 show the mortality table stepping at the 계약해당일: claims_death moves from 487.5506 to 534.0717 at 만나이 65 and from 1,412.0604 to 1,546.9336 at 80, because q(x) increments once a year and the account is large. claims_lump(240) = 101.8715 is below claims_lump(239) = 139.1227 for a reason worth naming: the 1·2등급 share s_g2 is falling with age through this range — 0.1270 at 72 down to 0.1110 at 82 — and the negative s_G' term of the product rule bites hardest where the share is steepest. The claim rate on a severe threshold does not rise monotonically with age even though the all-grade certification rate does.

t = 600 is the 90세 계약해당일: pols_if(600) = 0.2102 reaches it and is paid nothing.

Undiscounted totals, t = 0 … 600#

column

total

pols_if

343.1313

pols_act

341.3953

pols_healthy

330.6077

pols_light

10.7877

pols_care

1.7360

premiums

973533.0572

claims_lump

268065.6927

claims_annuity

546912.1402

claims_dementia

0.0000

claims_death

326783.9323

claims_lapse

70149.7799

claims_void

0.0073

claims_maturity

0.0000

expenses

135756.2503

claim_expenses

3774.5847

commissions

70945.8826

net_cf

-448855.2128

Policy year 1 in aggregate (t = 0 … 11, all at 만나이 40, all in policy year 1 — the strongest single test target in this file, because it exercises the whole annual cycle on one set of rates):

line

policy year 1 total

pols_if

11.548279

pols_act

11.548268

pols_light

0.000538

pols_care

0.000011

premiums

64670.302783

claims_lump

15.974040

claims_annuity

2.900270

claims_death

22.769436

claims_void

0.007271

expenses

31429.655856

claim_expenses

0.091280

commissions

43680.000000

net_cf

-10481.095370

(The totals are sums of unrounded monthly values; the thirteen displayed rows do not re-add to them.)

Decrement and state totals over the whole projection, per policy issued:

quantity

value

lives ever certified at the benefit grade, Σ pols_entry_care

0.026808014544

lives voided inside the 보장개시일 window, Σ pols_void

0.000000626279

cumulative deaths, Σ pols_death

0.354308072159

— of which not yet certified, Σ pols_death_act

0.337733821029

— of which in the care state, Σ pols_death_care

0.016574251130

cumulative lapses, Σ pols_lapse

0.435534876925

reaching the 90세 계약해당일, pols_if(600)

0.210156424636

간병연금 instalments paid, Σ ann_count

1.453879542900

annual proof-of-life events, Σ ann_tests

0.099011476675

Present values at the 예정이율 of 2.0%#

The model does not publish these; they are the calibration check that the premium, the incidence basis and the expense basis are mutually consistent. claims_dementia and claims_maturity are zero, so the nine lines re-add to net_cf.

line

PV

premiums

814356.0041

claims_lump

120884.7459

claims_annuity

253930.5911

claims_death

166819.3187

claims_lapse

38211.9050

claims_void

0.0073

expenses

97088.7515

claim_expenses

1746.6060

commissions

66187.8032

net_cf

69486.2754

PV(lump + annuity) / PV(premiums)

0.4602598067

PV(expenses + claim exp + commission) / PV(premiums)

0.2026425297

What the numbers say#

This contract prefunds a cost that essentially does not arise until the block is old, and then pays it out mostly as something other than the benefit it is sold for. Year-1 benefit outgo is ₩18.87 against ₩64,670 of premium — 0.029% — because the direct entry rate at 만나이 40 is one in 450,000 a year and the progression rate applies to a light compartment that barely exists yet. By 만나이 85 the all-grade certification prevalence is 20.5% and the model’s own first-entry rate into 1·2등급 is 0.70% a year, a factor of 30 on the age-65 rate. 39.1% of lifetime benefit outgo falls at attained age 85 or over and 63.3% at 80 or over — and the 90세만기 truncates the exposure at exactly the band with the highest certification rate of all. Over fifty years only 2.68% of the cohort is ever certified at the benefit grade, against 43.6% who lapse and 35.4% who die.

Three consequences follow, and they are what distinguishes this product from its Japanese counterpart rather than from the chassis. First, lapse and the interest rate, not the incidence basis, are the dominant levers: the lapse assumption removes 43.6% of the block before the claims arrive, and on the level 표준형 comparison vector — 4.0% at every duration against a log-linear path that falls to 0.1% — lifetime benefit outgo falls from ₩814,978 to ₩317,016, a 61% cut, on a basis change the regulator explicitly polices REG-R27. It is the right instinct for a supervisor to have had.

Second, the 계약자적립액 is the third-largest cash flow in the statement. claims_death is ₩326,784 undiscounted, a third of premium income and larger than the lump sum, because 35.4% of the cohort dies before maturity with an account worth close to cumulative premiums. This is not a death benefit and this contract has none; it is 감독규정 제7-63조제1항제1호 in operation REG-R17, and a reader arriving from a UK or US long-term-care model will not expect it.

Third, the 간병연금 is two thirds of the benefit — ₩546,912 against ₩268,066 — even though it is the optional rider and the lump sum is the main contract, and it is the reason the post-onset survival basis matters here in a way it does not on the chassis. On a lump-sum-only run of the same cell, undiscounted benefit outgo is ₩268,066 and net_cf turns positive at +₩101,027. The whole of this contract’s economic content sits in the module whose central assumption — how long a Korean life survives after certification — is the one thing nobody publishes.

Valuation and reserve pointers#

This library projects gross, undiscounted 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 over one stream at the same time, live rather than prospective.

  • K-IFRS 제1117호 (IFRS 17), mandatory for Korean insurers from 2023-01-01 REG-R60. The projected stream is the fulfilment cash flow before discounting and the risk adjustment; the CSM and its release pattern are out of scope. The contract boundary question does not bite on this product the way it does on Medical_KR_S, because the long-term-care benefit is written 비갱신형 on every retrieved document [S1] [S2].

  • The 계리가정 guidance reaches this model directly and by name. The FSS’s November 2024 ruling on 무·저해지 lapse assumptions REG-R27 is not background: it fixes the functional form of lapse_rate(t) and two of its three parameters, and 63.8% of Korean 보장성 초회보험료 in 2024 H1 was written in a 무·저해지 form. The pyojun comparison vector is shipped because the guidance requires an insurer using anything other than the 원칙모형 to disclose the difference in CSM, best-estimate liability, K-ICS ratio and net income quarterly. The instrument itself was not retrieved and the functional form is unverified at instrument level R14, secondary.

  • K-ICS, in force from the same quarter REG-R13, with the 경과조치 regime and the 적기시정조치 thresholds of 제7-17조~제7-19조 REG-R14. LTC_KR_S computes no required capital. What it owes the regime is a projection re-runnable on a re-set assumption basis at a stated 기준일, which the Projection Space’s scalar References provide. The 대량해지 shock of [별표 22], including the 고환급형 test, was not retrieved and anything resting on it is second-hand and unverified REG-R26.

  • 해약환급금준비금, which has no counterpart anywhere else in this repository REG-R11. It is a distributable-earnings device sitting on top of the IFRS 17 balance sheet and it is large on exactly this product shape: a 미지급형 contract has a nil statutory surrender value for twenty years and a large one the day after, so the difference the reserve is measuring moves discontinuously at 납입완료. av_pp and cv_pp are published per policy so that the layer above can be built on them.

  • 표준책임준비금 and 순보험료식 적립. 보험업법 제120조 requires the 책임준비금 REG-R3; 감독규정 제6-11조 and following set the accumulation REG-R10; 제7-64조 and 제7-65조 govern the 산출방법서 and the 계약자적립액 REG-R18; 제7-66조 through 제7-70조 govern the 해약환급금 and extend the regime to 제3보험 REG-R19. One surrender-value regime governs all ten krlib products, which is why this document inherits the chassis’s rather than restating it. 보험업법 제181조 and 제184조 then put the basis and its verification inside the 선임계리사’s statutory duty REG-R5; the tables here are a reference implementation’s, not an appointed actuary’s.

  • 제3보험 design rules. 감독규정 제7-63조 is the article that makes claims_death exist at all REG-R17, and 보험업법 제4조제1항제3호 is what makes 간병보험 a 보험종목 in its own right rather than a species of 질병보험, writable by life and non-life carriers alike REG-R1 REG-R7 R12 — which is why the five documents behind this composite come two from life carriers, two from non-life carriers and one from a state insurer outside 보험업법 altogether.

  • Policyholder tax, not modelled. Premiums fall in the 보장성보험료 세액공제 basket — a 12% credit on up to ₩1,000,000 of annual premium, so at most ₩120,000 of relief [S1] REG-R57, 15% under the 장애인전용보험전환특약 [S1] [S2]. A credit, not a deduction, which is the distinguishing feature of the Korean personal tax treatment throughout krlib: it is worth the same to a high-rate and a low-rate taxpayer, and worth more to the latter as a fraction of premium. The anchor’s ₩67,200 annual premium is well inside the cap. Benefits are not projected net of policyholder tax. On insurer failure contracts are protected under 예금자보호법 to ₩100,000,000 from 2025-09-01, on the 시행령 제18조 basis REG-R32 REG-R52.

Key sensitivities and model risks#

In rough order of leverage on this block. Every figure is a re-run of the shipped model on the anchor cell with one thing changed, and says what was changed.

  1. The care-state mortality multiple, twice over. care_mort_mult sets how long the annuity runs and it is the excess-mortality term of the incidence identity, so it moves entry and run-off in opposite directions at once. Setting it to 1.0 — the “there is no impaired-life table so leave it alone” choice — cuts lifetime lump-sum claims by 37.7% (₩268,066 → ₩166,938) and annuity claims by 14.7%, and cuts lives ever certified from 0.026808 to 0.016695. At 2.0 the cuts are 19.2% and 6.6%; at 4.0 lump-sum claims rise 20.1% and annuity claims 5.6% — note that even the annuity rises, because the extra entrants outweigh the shorter run-off at this multiple. There is no published table anywhere and the derivation behind 3.0 rests on a 4-to-5.5-year duration bracket that is itself derived. This is the model’s largest quantified sensitivity.

  2. The calibration gap against the disclosed 예정위험률. The model’s own first-entry rate is 24.0% of the one disclosed Korean long-term-care incidence rate at 만나이 40, 24.7% at 50 and 24.0% at 60 [S1] — the disclosed rate is about 4.2 times the model’s best estimate. Four biases all run the same way and none is quantified: a 예정위험률 is a loaded pricing rate; the conversion reads a cross-section as a cohort path in a scheme that grew 71.8% in six years; the care compartment leaves only by death when 9.2% of certifications came from a 등급변경신청; and the card is on 보험나이. Scaling the model’s basis up to the disclosed rate would multiply benefit outgo by roughly four and make the [S2]-derived premium impossible, which is itself evidence that the disclosed rate is not a best estimate — but the gap is not closed here and it should not be treated as resolved.

  3. The 보험기간 truncation at 90. Running the same cell to 100세만기 raises undiscounted lump-sum claims 70.6% (₩268,066 → ₩457,418) and annuity claims 59.3% (₩546,912 → ₩871,368), and PV benefit outgo at 2.0% by 46.9%, taking PV(benefit)/PV(premium) from 0.4603 to 0.6762 on an unchanged premium. 95세만기 is +41.2% / +37.4%. The composite stops at 90 because that is the modal Korean maturity and the term of both published rate anchors [S1] [S2], but it truncates the exposure at the band with the highest certification rate of all — 41.7% at 85+, and still rising — and it is materially conservative on claim cost. This is the first sensitivity a user should run.

  4. Lapse, and note that its sign here is the opposite of the naive one. Switching to the pyojun comparison vector — a level 4.0% at every duration, against a log-linear path from 8.0% falling to 0.1% at 납입완료 — cuts lifetime benefit outgo by 61.1% (₩814,978 → ₩317,016) and turns net_cf from −₩448,855 to +₩120,120. The level vector looks lower than the first-year rate but is far higher on average over fifty years, so it removes most of the block before the claims arrive. A model whose lapse assumption is described only by its first-year value cannot be read at all on this product. Only the 8.0% first-year level is std; the shape and the two convergence points are the regulator’s REG-R27.

  5. direct_entry_share — timing, not level. At 0.05 lifetime benefit outgo rises only 0.7% (₩814,978 → ₩821,073) and at 0.50 it falls 1.8%; but PV at 2.0% moves from 0.4653 to 0.4485 of PV premium, and the shape of the run-off moves far more than the total. That is the expected behaviour of a parameter that reallocates one inflow between two routes with different delays, and it is why the closing assumption is defensible even though it is unsourced: it is not carrying the level.

  6. The prevalence ceiling matters less here than on the Japanese counterpart, and the reason is the term. Refitting the male logistic through the same five sourced anchors at prev_ceil = 0.50 gives (beta, x_mid) = (0.15902124, 87.333743) and lifetime benefit outgo of ₩819,113 (+0.5%); at 0.35, (0.17495141, 83.544175) and ₩812,896 (−0.3%); at 0.95, (0.14221416, 94.063820) and ₩812,401 (−0.3%). The total barely moves because a lower ceiling refits to a steeper beta and buys back before 85 what it gives up after, and because a 90세만기 contract never reaches the region where the ceilings differ. On a 100세만기 or a 종신 variant this sensitivity would be first-order and it is not tested here. Nothing above 만나이 88.5 is sourced.

  7. The grade share, and what “up to a factor of two” means. Replacing the age-varying s_g2 with the national all-ages figure of 0.1328 moves lifetime benefit outgo only +0.8%, but it moves the split: lump-sum claims −3.2% and annuity claims +2.7%, and it re-times both. The factor of two is a statement about the rate at a given age — 0.222 below 65 against 0.111 at 80–84 — not about the anchor cell’s lifetime total, and a product issued at 60 to a 1등급 threshold would feel it far more.

  8. The 감액기간, and why it is nearly worthless on this cell and not on others. Setting red_mths = 0 moves lifetime benefit outgo by +0.010% and red_mths = 24 by −0.023%, because at issue age 40 almost nothing is certified in the first year or two. It is not a negligible mechanic in general: see the pitfall below on freezing it, where the same mis-modelling is worth 0.31% of annuity outgo at issue age 70 and 0.01% at 40. A parameter that does nothing on the anchor cell can still be a first-order error at the top of the issue-age range, which is why the anchor cell is not the only test target.

  9. The 간편심사 loading is pure margin in this model. Model point 8 carries uw_loading = 1.40 on a premium already set at the risk level, and the model has no separate incidence basis for the simplified-underwriting pool because no retrieved source gives one. Its positive net_cf of +₩1,152,142 is an artefact of that and must be described as one. The true claim cost of a simplified pool on this trigger is understated, and one carrier’s refusal to attach its 장기요양 riders to a simplified chassis at all [S1] is the market’s own view of how much.

  10. Longevity, not mortality, is the tail risk. On a living-benefit product longer survival means more entrants and more instalments. This model’s healthy mortality is anchored on an insured 기대여명 REG-R33 and is therefore lighter than the chassis’s population anchor REG-R38; that is the right direction here, but the anchor is a single summary statistic per sex and the shape between the ages is a Makeham–Gompertz assumption with two std parameters.

  11. Basis-change risk the insurer does not control, and cannot price. The grade thresholds, the scoring instrument and the very existence of the grades are set by 대통령령 REG-R55. The 인지지원등급 was created out of nothing on 2018-01-01 R6 and enlarged the covered population of every 「1~인지지원등급」 rider overnight at no additional premium. What the contracts carry against this is a contract-continuity clause [S3] and a successor-body definition [S4], not a repricing right. The asymmetry is unquantifiable, it has no counterpart in jplib, frlib or uklib whose triggers are contractual, and it is the reason a Korean insurer’s real exposure on this product is wider than any sensitivity in this list.

  12. A stock that is still growing. The certified population grew 71.8% between 2018 and 2024 while the 65+ population grew 36.6% R4 R16, so roughly half the growth is demographic and half is a rising rate — driven partly by the 2018 creation of 인지지원등급 and partly by the scheme’s continuing maturation. The stationary-population reading of the cross-section is therefore known to understate entry, and the model does not project the trend.

Known modeling pitfalls#

Each of these is a mistake a modeller would actually make on this product, and each is stated so that it can be checked.

  • 인정률 is a prevalence, not an incidence — and the ratio is not a constant. 10.85% of the 65+ population held a certification at end-2024 R4; 1·2등급 prevalence at 만나이 65 is 0.246%. The model’s own first-entry rate at the same age is 0.02343%, so the prevalence is 10.5 times the incidence at 65, 6.5 times at 75 and 3.8 times at 85. Multiplying an 인정률 by a benefit amount, or treating it as an annual claim frequency, is the single commonest error in a Korean long-term-care model, and using one ratio to convert it at every age is the second commonest.

  • The excess-mortality term of the identity is not a refinement, and neither is mu_bar. Setting care_mort_mult = 1 drops the term entirely and cuts lifetime lump-sum claims by 37.7%. Keeping mu_C but dropping mu_bar — using P_C × mu_C instead of P_C × (mu_C − mu_bar) — goes the other way and inflates the inflow at 만나이 65 by 8.2%. Prevalence is a proportion of a living population, so the comparison is against the population’s own average force, not against zero.

  • Take P_C' by the full product rule. P_C = s_G(x) P(x) and s_G is falling with age over most of the range for a severe threshold. Dropping the s_G'(x) P(x) term leaves s_G(x) P'(x), which at 만나이 65 is 1.82× the correct P_C' and at 75 is 1.19×. The visible symptom is that claims_lump rises monotonically with age, whereas the shipped model has it falling between t = 239 and t = 240 (139.1227 → 101.8715).

  • The 감액 is frozen at first certification and must not be re-tested at each instalment. 「최초 진단 확정일을 기준으로 … 그 이후에 도래하는 매년 진단 확정일이 계약일부터 2년이상에 해당하더라도 … 지급액은 변경되지 않습니다」 [S1]. A model that re-tests it pays the full amount from month 12 onward to cohorts certified in the first year, overstating annuity outgo by ₩64.78 on the anchor cell (+0.012%), by ₩596.60 at issue age 60 (+0.097%) and by ₩1,065.24 at issue age 70 (+0.315%). Evaluate red_factor at s, never at t.

  • The annuity’s first instalment falls in the month of certification. The u = 0 term of ann_count(t) is n_C(t) itself [S1]. Deferring it by twelve months removes roughly a tenth of the annuity liability and misdates all of it. Related and opposite: the instalments are monthly while the survival test is annual, so a model that pays annually gets the amount right and the timing wrong, and a model that tests survival monthly gets the timing right and the amount wrong.

  • The claim expense is per event, not per instalment. The proof of life the 약관 requires is annual — 「매년 진단 확정일에 피보험자의 주민등록등본을 제출하여야 합니다」 [S1] — so ann_tests totals 0.0990 over the projection against ann_count’s 1.4539. Charging ₩30,000 per monthly instalment would multiply the annuity’s claim expense by about fifteen.

  • Compute care_surv as a partial product, never as a ratio of cumulative products. mort_rate_care is capped at 1 and the cap binds from 만나이 108 on the shipped male table and 112 on the female one, so a cumulative product underflows to zero from there on and the ratio form divides by zero exactly where the tail of a 종신 variant lives. It does not bite on any shipped model point, which is precisely why it would be found late.

  • Premium rides on pols_act, never on pols_if. Charging the whole in-force block overstates lifetime premium income by ₩414.65 on the anchor cell, 0.043% — small because the certification rate at issue age 40 is small, and much larger at the top of the issue-age range. Note that the error here is the reverse of the Japanese product’s, where the waiver fires below the benefit and the band is large: here G_W = G_B, so the only lives on waiver are lives already claiming.

  • Do not apply lapse to the care compartment, and know that the check will not catch you. The premium is waived [S3] and the 약관 bars surrender [S1]. Applying the lapse rate to pols_care as well leaves claims_annuity completely unchanged at ₩546,912.14 — the ledger is driven by n_C and care_surv, not by the compartment — and check_pols_roll_fwd() still closes, because the roll-forward is consistent. The only visible effect is ₩489.73 of extra claims_lapse, a surrender value paid to lives the contract forbids from surrendering. It is a silent error and the reason cv_pp and pols_lapse should be read together.

  • A certification inside the 보장개시일 window is a decrement, not a deferred claim. 「특약을 무효로 하며, 이미 납입한 보험료를 돌려드립니다」 [S1] [S2]. The life leaves the model with a refund; it does not sit in the block waiting for the window to close. And there is no cancellation option and no revival here, unlike the cancer chassis, so a model that imports the chassis’s 90-day cancellation right invents a term this product does not have. And the refund is cum_prem_pp(t + 1), not cum_prem_pp(t): premium falls at the start of month t and the void at the end of it, so a life voided in month 0 has paid one month and gets it back. claims_void(0) is ₩0.001040 and claims_void(3) is nil — for opposite reasons, the second because the window has closed.

  • The surrender-value cliff has a direction, and three of the four Korean forms differ only in which side of 납입완료 the 50% attaches to. 미지급형 is nil during and 50% of a notional 기본형 after [S2]; 납입중50%해약환급금지급형 is 50% during and 100% after [S4]; 표준형 pays the full account less the 해약공제액 from year 1 [S1]. Getting the side wrong inverts the whole cash-flow shape and is not caught by any total. check_cv_form() asserts cv_pp(t) = 0 identically for t < n_P on the 미지급형 form, with its sign, for exactly this reason.

  • claims_death is not a death benefit. This contract has none [S1] [S3]. It is the 계약자적립액 that 감독규정 제7-63조제1항제1호 makes payable on a death from a cause the contract does not cover REG-R17, and at ₩326,784 undiscounted it is a third of premium income and larger than the lump sum. Reading it as a sum assured, or dropping it because “this is a pure protection contract”, are both wrong and in opposite directions. And deaths in the care state pay nothing — 「지급사유가 발생한 후 사망한 경우에는 별도로 책임준비금을 지급하지 않습니다」 [S1] — which is why pols_death is split; on the anchor cell 0.0166 of the 0.3543 cumulative deaths pay nothing.

  • The light compartment pays premium and lapses; the care compartment does neither. Collapsing the two into one “certified” state either stops a premium the contract goes on charging or invents a benefit at a grade it does not cover, and — the larger error — turns the 1·2등급 rate into a healthy-life incidence. On the shipped basis progression overtakes direct entry by policy month 8 at issue age 40, and above 65 it is 80% of gross inflow by construction. A single-decrement model puts the cash flow years too early.

  • prog_rate_at is not scaled below 65 and that is deliberate. sub65_factor_at applies to i_D and i_L, which are rates of entering the scheme through a gate the statute narrows below 65; rho is a property of a life already certified, and a life certified at 만나이 50 got there through the 노인성 질병 list and is, if anything, more likely to progress than a 70-year-old. rho(40) = 0.0340 is therefore higher than rho(65) = 0.0153, which looks wrong on a decrement table and is right here.

  • Widening the threshold is not a re-scaling. Moving benefit_grade from g2 to g5 on the anchor cell takes lifetime benefit outgo from ₩814,978 to ₩1,978,328 — a factor of 2.43 — and PV(benefit)/PV(premium) from 0.4603 to 1.1233, on an unchanged premium. Moving it to g1 gives 0.1997. The exposure changes in frequency and in timing together, because the light compartment shrinks as the gate widens and vanishes entirely at g6. Treating the threshold as a multiplier on one incidence rate is the error the market itself prices against at about 4.5 : 1 [S2, derived].

  • The two modules run in opposite sex directions and the model does not reproduce that. 장기요양 covers are dearer for women at every age (여/남 = 1.52 at 40 on the main contract) and 치매 covers are cheaper (0.80 on 경도이상치매), in the same document [S2, derived]. The certification basis reproduces the first through the sourced prevalence; the dementia basis applies a flat-in-age sex factor R7 and therefore does not reproduce the second. A user who switches the rider on and reads the sex differential off the output is reading an artefact of that simplification.

  • The care state is absorbing because the contract makes it so, not because the state is. Grades move both ways — 107,365 of 1,165,030 current certifications came from a 등급변경신청 R4 표2-5 and one carrier drafts a rider around exactly that [S3] — but the amount is frozen at first certification, the instalments are metered on survival rather than on continued certification, and surrender is barred [S1]. So the simplification is smaller here than it looks. It would not be available at all for the utilisation-conditioned 지원금 form [S2], which requires the insured to be using a named public benefit in the month; a model that ported this chassis to that product without a utilisation and recovery basis would be materially wrong.

  • Do not read the disclosed 예정위험률 as a level. It is used here for its gradient below 65 and its sex ratio, and disclosed_inc_ratio_at publishes the gap rather than hiding it. Substituting it as the model’s incidence would multiply benefit outgo by roughly four and contradict the premium it was quoted alongside.

  • proj_len() is a row count, not the last index. result_cf() has proj_len() = 601 rows indexed t = 0 … 600, and the last of them is the 90세 계약해당일: an in-force count of 0.2102 and every cash flow zero. The frame is range(proj_len()) and the maturity row is t = proj_len() − 1, which is why the cash-flow cells guard on t >= proj_len() - 1 while the in-force counts guard on t >= proj_len(). Writing the cash-flow guard as t >= proj_len() would put outgo on the maturity row; writing the count guard as t >= proj_len() - 1 would drop the row the roll-forward closes on and break check_pols_roll_fwd() at the last step.