Implementation Notes#

Status: Draft, 2026-09-03. Built from technical-notes.md (the product as a liability cash flow projection on paper) and product-spec.md (the representative contract those notes model). Source tags resolve against sources.md.

This is a mechanics demonstration, not a pricing or reserving result. The contractual mechanics are sourced: the charge schedule as percentages of the 기본보험료 (gibon boheomryo, basic premium) [S1], the nil 해약공제액 [S1], the death benefit as the 계약자적립액 (gyeyakja jeongnibaek, policyholder account value) and nothing more [S1] [S2] [S4] [S6], the 100.1%-of-premiums minimum fund at the 연금개시일 [S2] [S4] [S7], the two annuity forms and their two different bases [S1] [S2] [S6], the 0.5% 연금수령기간 관리비용 [S1] [S7], and the 공시이율 / 최저보증이율 machinery [S1] [S2] [S4] [S13] REG-R16 REG-R18. The mortality basis is not a published table. 경험생명표 is produced by 보험개발원 and released only as summary statistics REG-R33 REG-R34 R16 R17, so mort_table.csv is a std construction and says so on every row. The lapse curve, the best-estimate mortality factor, the cash expenses and the policy-loan rate are standardizations. Replace them all with company data, and the mortality with the filed 산출방법서 basis, before drawing any conclusion from the numbers.

Pension_KR_S is the monthly-grid model of the tax-qualified pension savings composite (yeongeum jeochuk boheom, 연금저축보험). It inherits the surrender-value machinery of the whole life chassis (종신보험) — the 해약공제액, its statutory cap and the 해약환급금 floor — but not that chassis’s 계약자적립액 recursion, which is a net-level accumulation with a survivorship release where this one is a plain account (next section). It adds the five things the notes specify for the first time in the library: crediting at a declared rate over a guaranteed floor, the tax layer as a behavioural driver rather than a cash flow, the statutory 연금수령 conditions as constraints, the annuitisation step, and the question of which vintage of the annuitant table the factor is struck on.

Run it#

python products/pension_savings/run.py            # the worked example's anchor cell
python products/pension_savings/run.py 9          # another model point

run.py prints the model point and its module switches, the annuitisation quantities, the head and tail of result_cf(), the undiscounted totals and every check_*() cells. Its output is ASCII only, so it prints on a Windows console under any code page: amounts are written KRW and Korean terms are romanized. Real output below, abridged to fit the page: middle rows and the all-but-constant claim_expenses, commissions and policy_loans columns are dropped, the header lines are re-wrapped, and a few parenthetical glosses and the two all-zero module and dividend fields are trimmed. No figure is changed; run run.py for the unabridged text.

model point 1: KR-PEN-0001 - yeongeum jeochuk boheom (tax-qualified pension savings), M40
age basis boheom nai (insurance age); t counts completed policy MONTHS from issue, 0-based
frame t = 0 .. 971 (972 rows, 81 policy years); policy year = t // 12 + 1
gibon boheomryo (basic premium) = KRW 500,000/month (6,000,000 p.a.) for 20 years,
    chuga nabip (additional) = KRW 0 p.a.
premium term ends at t = 240, annuity starts at t = 300 (age 65), payout form = jongsin
    yeongeumhyeong (life annuity) with a 10-year guarantee
modules: mortality vintage = issue   100.1% minimum fund = True   surrender charge = 0.00%
         payment holiday = 0 yrs   policy loan = False   participating = False
         lapse basis = pension   rate scenario = base   gongsi iyul at t=0 = 2.15%

cumulative premiums to t = n     = KRW 120,000,000.00
gyeyakja jeongnibaek AV(n)       = KRW 160,294,805.59
100.1% minimum fund              = KRW 120,120,000.00
annuity fund F, after the floor  = KRW 160,294,805.59
annuity-due factor               = 23.58191602
yeongeum yeonaek B               = KRW 6,763,375 p.a. (KRW 563,615 a month)
implied factor F_net / B         = 23.7004
pyojun haeyak gongjeaek (cap)    = KRW 1,421,988.72
haeyak hwangeupgeum CV(12)/prem  = 96.61%
seaek gongje (tax credit) p.a.   = KRW 990,000  [not an insurer cash flow]
gita sodeukse on surrender at 10y= KRW 10,590,733  [not an insurer cash flow]

cash flow statement, KRW per policy issued per month, income positive
   pols_if   premiums  claims_annuity  claims_death  claims_lapse   expenses     net_cf
t
0     1.00  500000.00            0.00         32.16       1624.38  202500.00  295841.44
1     1.00  498268.47            0.00         64.16       3240.39    2491.34  492470.57
...
300   0.61       0.00       343630.80          0.00          0.00    1667.10 -345297.90
...
971   0.00       0.00           58.79          0.00          0.00       0.85     -59.63

undiscounted total premiums      = KRW 94,113,902.70
undiscounted total annuity outgo = KRW 134,873,106.96
undiscounted total net_cf        = KRW -66,447,581.54

check_pols_roll_fwd()    True
check_av_roll_fwd()      True
check_cv_floor()         True
check_surr_chg_cap()     True
check_min_fund()         True
check_annuity_total()    True
check_annuity_limit()    True
check_mort_law()         True
check_net_cf()           True

Three lines to the same thing:

import modelx as mx
model = mx.read_model("products/pension_savings/Pension_KR_S")
model.Projection[1].result_cf()

Projection takes a point_id; Projection[1] is the anchor cell of the notes’ worked example. result_cf() returns a DataFrame indexed by the 0-based policy month index t, running t = 0 … proj_len() - 1, with pols_if first and net_cf last. result_pols() publishes the decrement and value runs beside it — the two in-force measures, the decrements that move them, and the fund, surrender value and cumulative premiums that price them — which is where the 환급률 a Korean illustration quotes becomes legible. result_tax() prints the tax layer, which is not a cash flow of the insurer and is in a frame of its own for that reason. model.Projection.doc carries the notes’ symbols mapped to the cells names.

The fund is an account, and there is no mortality in it#

This is the structural difference from the two nearest accumulation models in this repository, and it is not a parameter difference. Annuity_JP_S’s 保険料積立金 is a net-level-premium reserve with a survivorship release: the premiums of those who die go to the survivors net of the death benefit paid, so the recursion divides by (1 - q'). So — and this is the trap, because it is the nearer neighbour and shares the Korean name — does WholeLife_KR_S’s own 계약자적립액, which runs V(d) = ((V(d-1) + P·1{d <= m})(1 + i) - q·SA)/(1 - q), on that model’s anniversary index d (d = 0 at issue), not on this model’s period index t. This 계약자적립액 does none of that. It is a contractual balance:

AV(0)   = 0
AV(t+1) = ( AV(t) + NP(t) - C(t) ) ( 1 + j_c(t) )

a month at a time, with j_c(t) = credit_rate_mth(t) = (1 + i_c(t))^(1/12) - 1, and check_av_roll_fwd asserts exactly that identity. NP(t) is the monthly 순보험료 — the month’s 기본보험료 less both published charges, 「「계약자적립액」이란 순보험료(기본보험료에서 계약체결비용 및 계약관리비용을 뺀 금액)를 「공시이율」로 … 적립한 금액」 [S1] [S2] — and C(t) is the charge taken from the fund in a month when no premium bears it.

There is no survivorship release because there is nothing to release. Every retrieved life-insurer 연금저축보험 pays the fund and nothing more on death before annuitisation — 「사망 당시의 계약자적립액을 지급하여 드리고 이 계약은 더는 효력이 없습니다」 [S1] [S2] [S4] [S6] — and 감독규정 제7-60조제9호’s requirement of a death benefit of at least cumulative premiums exempts a contract whose premium term ends at 80 or below REG-R16, which this one does at 60. So the insurer’s deferral-phase mortality strain is exactly zero, and with the composite’s nil 해약공제액 the death payment and the surrender payment are the same number at every duration: claims_death and claims_lapse differ in their decrement rate and in nothing else. A model that applies a decrement-weighted death strain here is projecting a strain of zero and should say so rather than compute it.

Mortality enters this contract in one place, annuity_due_factor_on, and it is a longevity exposure that begins at the 연금개시일.

The horizon is the annuitant table’s terminal age, and `proj_len()` is a count#

The time index t is 0-based and counts policy months: t = 0 is the first projected policy month, age(t) is x + t // 12, pols_if(0) is pols_if_init(), and the contractual policy year is the derived 1-based label policy_year(t) = t // 12 + 1. The contract has no maturity date, so nothing in it fixes a horizon; proj_len() derives one from the payout form and it is the number of projected months — the frame’s exclusive end, range(proj_len()) — so the last index is proj_len() - 1. proj_years() carries the same horizon in years and proj_len() is always 12 * proj_years().

On the 확정기간연금형 the contract pays exactly 12k instalments and ends, so proj_len() = n + 12k and there are no tail states at all. Model point 5’s last row is 479.
On the 종신연금형 there is no natural end, so the horizon is the terminal age of the annuitant table less the issue age — the last policy year at whose start anyone can still be alive. At the anchor cell that last year is 120 - 40 = 80, so proj_years() is 81, proj_len() is 972, result_cf() has 972 rows running t = 0 … 971, and the terminal policy year is where q reaches 1.

ω = 120 is a std: no Korean industry table publishes a terminal age, because no Korean industry table is published at all REG-R33 REG-R34. It costs almost nothing to be generous with it — the last five policy years of the anchor cell’s projection carry 0.0249 of combined in-force and ₩170,814 of outgo, 0.12% of the annuity total — while a horizon short enough to bite would silently truncate a life annuity’s tail. Sweeping range(proj_len() - 1) — the off-by-one of reading the exclusive end as the last index and then subtracting — drops exactly that terminal row; the slip in the other direction, range(proj_len() + 1), appends an empty row at t = 972 instead.

At the terminal age the table’s q is 1, which a monthly grid cannot apply as a monthly rate. mort_rate_mth spreads the certain death uniformly over the twelve months of that policy year — 1 / (12 - t mod 12), so 1/12 in month 960 rising to 1 in month 971 — which is the uniform distribution of deaths and is what makes the last row of the frame the row where the in-force actually reaches zero.

The monthly grid, and the annual assumptions on top of it#

Every retrieved contract is 월납, interest accrues 「납입일부터 일자계산을 하여」 — from the date each instalment is received, not from the anniversary [S1] [S2] — the account accrues monthly before 납입완료 under 감독규정 제7-66조제1항제4호 REG-R19, and the annuity is paid 매월 [S1] [S2] [S5] [S6] [S7]. The model runs a monthly grid, so each of those is followed directly. The annual grid this replaced ran under the separate annualised-premium permission of 감독규정 제7-65조제2항, 「계약자적립액은 … 연납보험료를 기준으로 하여 산출할 수 있다」 REG-R18 — a filed-basis convention rather than a shortcut, but one the monthly grid does not need.

The assumptions stay annual and only the grid gets finer. credit_rate(t), mort_rate(t) and lapse_rate(t) are the annual figures the technical notes tabulate — a 공시이율 is declared as an annual rate, the 연금사망률 is an annual table by age, and the lapse vectors are annual by 경과기간 — and the projection applies their uniform-force companions:

credit_rate_mth(t) = ( 1 + credit_rate(t) ) ** (1/12) - 1
mort_rate_mth(t)   = 1 - ( 1 - mort_rate(t) ) ** (1/12)
lapse_rate_mth(t)  = 1 - ( 1 - lapse_rate(t) ) ** (1/12)

Twelve of each compound back to the year’s figure exactly, so the fund and the in-force at every 계약해당일 reproduce the annual-step model this replaced — av_pp to a relative 1.4e-14, pols_if to the last printed digit. That equality is worth stating plainly: it means the sub-annual timing factor the annual grid carried, u(t) = (1/12) Σ (1 + i_c)^(−j/12) = 0.990316187680581 at 2.15%, was exactly right, and the monthly recursion has replaced it rather than corrected it. What the monthly grid adds is everything inside the policy year, which the annual grid had no way to state: a 환급률 of 95.67% after one month against 96.61% after one year, a ₩3,350 monthly charge in each of the sixty months between 납입완료 and 연금개시 instead of five annual ones, and a surrender dated to the month.

Two conversions are deliberately not made. The 세액공제 ceiling and the 연금수령한도 are per-year statutory figures and 별표 14’s 표준해약공제액 is struck on the 연납순보험료, so each is computed annually and apportioned across the year’s twelve months rather than restated on a monthly base the law does not use. And the 연금연액 B is the annual amount the contract quotes; annuity_pp(t) pays B / 12.

On the way out, the annuity factor is — and always was — the annuity-due payable twelve times a year. For the certain form that is exact, (1 - v^k) / d^(12); for the life form it is the annual factor less the standard (f - 1) / (2f) = 11/24 correction.

That last point is the single most consequential implementation decision in this model, because it is what makes the payout formula reconstruct the published illustration. [S2] publishes a fund at annuitisation and five annuities on two interest bases, and the implied factors are recovered as follows [derived]:

Form	Published implied	Model	Basis
확정 10년	9.06	9.061	공시이율 2.15%
확정 15년	12.92	12.918	2.15%
확정 20년	16.39	16.386	2.15%
확정 10년	9.81	9.806	최저보증 0.50%
확정 15년	14.53	14.528	0.50%
확정 20년	19.13	19.134	0.50%
종신 10년보증, 남 65	23.70	23.700	2.15%
종신 10년보증, 남 65	31.18	31.180	0.50%

All eight, on both interest bases, from one formula. Read on an annual annuity-due the same 계약자적립액 ÷ ä_n(공시이율) × (1 − 0.005) misses every one of these by about half a per cent in the wrong direction — it makes the annuity smaller than published where the published figure is larger than the textbook annual factor. That was the reading of an early draft of product-spec.md; technical-notes.md corrected it, its scope note records the change as a change to a number, and both documents now carry the monthly form. On the anchor cell the annual reading would give B = ₩6,634,429.17 against ₩6,763,374.59, 1.91% low.

The crediting machinery is four rates, not one#

decl_rate(t) is the 공시이율, the carrier’s declared rate. It is not a market rate and must not be modelled as one: 감독규정 제7-65조제3항 and 시행세칙 별표 27 build it from an external index rate and the insurer’s own 운용자산이익률 with the external weight capped at 60% REG-R18 REG-R24, so it is majority-weighted to realised investment return. One carrier’s published thirteen-month history falls 57 basis points over a year in steps of two to seven, never once reversing [S5]. The model therefore treats it as a slow-moving exogenous step function of policy year, read from decl_rate_table.csv by scenario — level across the twelve months of each policy year, not interpolated — and does not model the 조정률 at all, a discretionary carrier margin living in an unpublished 사업방법서.

min_guar_rate(t) is the 최저보증이율 ladder, 1.25 / 1.00 / 0.50 at five and ten years — months 60 and 120 on this grid — [S1] [S2] [S13]. It steps down with elapsed duration on every retrieved contract, so the guarantee is strongest exactly where the fund is smallest, and the ladder is a function of the product’s 판매개시일 rather than of the carrier — one carrier’s shelf runs two ladders side by side [S13].

credit_rate(t) is the greater of the two, and it is what the fund actually earns, through its monthly companion credit_rate_mth(t). The floor is a guarantee on the credited rate, not on the return: 「공시이율이 0.1%로 낮아지더라도 적립금은 … 최저보증이율로 적립됩니다」 [S8], and expenses are still deducted beneath it [S4]. That is why charge_from_av_pp never consults the floor.

A fourth rate is in the model and is neither of these. prem_int_rate is the 예정이율, 연복리 2.50%, the rate the charge and benefit structure was priced on [S1] [S5] [S7]; it is not a guarantee, its own sources say so, and it appears nowhere in the fund recursion. The library’s retired-name register keeps prem_int_rate and decl_rate apart for exactly this reason. A fifth, avg_decl_rate — the 평균공시이율, 2.50% for 2026 REG-R48 [S14] — is a supervisory average and enters only as a constraint, inside surr_chg_cap_pp.

The surrender value, and the statutory cap nobody uses#

cv_pp(t) = max(0, AV(t) - SC(t)), the floor being 감독규정 제7-66조제1항제1호 REG-R19, and check_cv_floor asserts it. On the composite SC(t) is zero at every duration, because the direct-channel product whose complete schedule the composite adopts publishes a 해약공제 table of all zeros [S1] — a design that recovers its acquisition cost entirely through the level monthly charge and has nothing left to claw back. So cv_pp == av_pp everywhere on the base run, which is a property of the adopted schedule and not of the product: model point 8 carries the state postal insurer’s front-end 해지공제액 instead, 8.67% of the annual premium at year 1 running off to zero at year 5 [S7], and the two separate. That schedule is published by policy year, so surr_chg_pp interpolates it linearly in the elapsed duration t / 12: the published amounts come back exactly at each 계약해당일, the first policy year carries the year-1 figure throughout, and between anniversaries the charge falls month by month instead of in four steps.

surr_chg_cap_pp computes 별표 14’s 표준해약공제액 and check_surr_chg_cap holds the charge inside it on every model point. The computation follows the notes to the letter: 주2 caps the 저축성보험 coefficient at a twelve-year premium term, 주3 defines the 연납순보험료 as the annual premium less the whole-term loading levelled over the payment term capped at ten years, 주5 replaces the general 5% with 3% for a 무배당 연금저축보험 and 4% if 배당 — par() reads this — and 주6 subtracts the acquisition amount loaded into the premium discounted at the 평균공시이율 REG-R20 R14. 주4’s 6% concession for a whole-of-life survival annuity is expressly denied to a 연금저축보험, and the second term of the formula, 보장성보험의 보험가입금액의 10/1000, is nil because the contract has no 보장성 element.

On the anchor cell the model returns ₩1,421,988.72, about 2.8 months of 기본보험료 and the order of magnitude 금융위원회 stated for a 저축성보험 in 2019 REG-R29. The composite uses none of it. That is the finding: the regulator has singled this product out for the tightest surrender-charge coefficient in the schedule, and the reference implementation sits far inside it. Where 주3 is read the other way — levelling only the first ten years’ loading rather than the whole term’s — the cap is ₩1,486,788.72, 4.56% higher; the model implements the first reading and the alternative is a one-line change to surr_chg_cap_pp.

The annuitisation transition, and which vintage of the table it is struck on#

At t = n the fund is fixed, floored at 100.1% of premiums paid, and divided by a factor.

The floor is real if shallow. 「연금개시시의 계약자적립액은 이미 납입한 보험료의 100.1%를 최저보증 합니다」 [S4 별표1 주10] [S2] [S7], with two more carriers writing the functionally identical 「이미 납입한 보험료 + 1,000원」 [S5] [S6]. Why 100.1% and not 100%: 감독규정 제7-60조제2호 requires a 저축성보험’s survival benefits to exceed premiums paid REG-R16. It is a survival guarantee — a death claim in deferral is not floored at premiums on this composite — and on the published guaranteed-rate illustration the fund reaches only 100.5% of premiums at the end of the twenty-year payment term [S2], so on a persistently low-rate path the floor is close to binding. check_min_fund asserts it. Model point 6 is the one shipped point where it binds exactly, at ₩30,030,000 against an av_pp(60) of ₩29,573,776.73; model point 9 carries it withdrawn, which is what the contracts do where a payment holiday or a one-instalment reinstatement caused the shortfall, deferring the annuity date instead [S4] [S6] [S7].

The factor is where the composite has to take a position the evidence does not settle. Six independently retrieved contracts carry the same clause — 「연금개시전에 연금사망률의 개정 등에 따라 연금연액이 증가하게 되는 경우 연금개시시점의 연금사망률 … 을 기준으로」 [S1 주6] [S2] [S4 별표1 주11] [S6 별표1 주10] [S9 별표2 주9] [S10 주4] — and every version shares two elements: the trigger is a revision that increases the annuity, and the substituted basis is the table 연금개시 당시. The clause is therefore a one-way ratchet in the policyholder’s favour, so the base factor must be something else, and the only candidate is the annuitant mortality in the 산출방법서 filed for the product — the table as at 가입. Two carriers publish the 연금사망률 in the 상품요약서 handed over at inception [S1] [S7], which corroborates it, as does trade reporting that a 경험생명표 revision reaches new business only R18 R20.

mort_vintage exposes all three readings:

Value	Behaviour	Model point
`issue`	the 가입시점 table; the composite’s reading	1–6, 8
`commencement`	the 연금개시시점 table	7
`ratchet`	the clause itself: whichever vintage gives the larger annuity	9

Because successive revisions have lightened mortality — the 제10회 raised 평균수명 by 2.8 years for men and cut the monthly annuity on a fixed fund by about 15% R18 R19 REG-R33 — a revision normally decreases the annuity, the ratchet does not bite, and ratchet returns the issue vintage. Model point 9 demonstrates that it does: mort_table_name() returns annuitant_issue, because the issue-vintage factor of 22.70113 is smaller than the revised-vintage 23.43728 and the smaller factor is the larger annuity. The vintage is worth 2.97% of the annuity (points 1 against 7), which is why it is a switch and not an assumption: a model that struck the factor on the 개시시점 table would understate the annuity, and a model that ignored the ratchet would be right in the base run and wrong under an improvement scenario.

The mortality table is a construction, and it ships with its recipe#

No qx table of any Korean industry basis was retrieved in either research pass. 보험개발원 holds the statutory office of 보험요율산출기관 under 보험업법 제176조 and files 참조순보험요율 with the supervisor with no publication obligation REG-R4 R16; the 제10회 경험생명표 is public only as 평균수명 남 86.3세 / 여 90.7세 and 65세 기대여명 남 23.7년 / 여 27.1년 REG-R33 R18 R19. The KIDI press-release page is JavaScript-driven and the release could not be opened R17 REG-R34; the big-data portal refused connections R24.

What is public, and what the table is anchored on, are the six annuitant rates two carriers publish in their statutory product summaries [S1] [S7]. mort_table.csv is a Makeham law mu(x) = A + B c^y with y = max(0, x − setback), fitted jointly to those six and to the annuity factors [S2] implies at two interest bases, with the parameters, the female setback, the vintage improvement factor and the six published anchors all recorded in mort_anchor_table.csv. check_mort_law re-derives every rate the projection reads from those parameters, so the day someone drops in a real basis the check reports it rather than the model silently claiming a construction it no longer has.

Three things about the fit are worth stating plainly, because they are the cost of taking the published illustration as the calibration target:

The two ä targets are met to four significant figures and the anchors are not. The model’s implied life factors are 23.7004 and 31.1799 against published quotients of 23.7000 and 31.1768 — inside the rounding of the 만원 figures [S2] publishes. The fitted male rates, by contrast, run about 30% above the published anchors at 70 and about 28% below at 80. A three-parameter law cannot honour a steep 60–80 gradient and a very light 65+ tail at the same time, and the annuity factor is dominated by the tail.
The implied longevity is extreme, and it is the illustration’s, not the model’s. The fitted table gives a male 65 a curtate expectation of life of 33.31 years against the 제10회’s own published 23.7 REG-R33 and 국가데이터처’s 완전생명표 19.5 REG-R38. That gap is what the calibration target requires: solving ä_n = 23.70 at 2.15% on the monthly annuity-due this model uses gives n ≈ 32.9, so the published life annuity is priced like a certain annuity running to about age 98 [derived] from [S2] — 32.5 and about 97 on the annual annuity-due, which is not the form this contract pays. A 연금사망률 is a pricing table loaded on the survival side for a longevity product, and this is what that loading looks like when it is read off a published annuity rather than assumed.
The female table is the male law set back four years, the whole-year setback closest to the published 65세 기대여명 gap of 3.4 years between the sexes REG-R33; it does not reproduce it — the model’s own gap is 3.66 years. The female published anchors are not reproduced either: the fitted female rates run 1.9 to 2.8 times the published ones at ages 50 to 70. The alternative — fitting the female law independently to the female anchors and to the one published female annuity illustration [S5] — was tried and rejected, because it comes from a different carrier on a different convention and produces a female annuity larger than the male’s at the same age, which no carrier’s rate card does. The sourced sex differential was preferred to the sourced female rates, and the reason is written on every female row of the file.

mort_be_factor is 1.15 and is greater than one deliberately. The table is a loaded pricing basis, so a best-estimate death decrement runs heavier than it, not lighter. The only direct evidence of the margin’s size is that the two carriers who publish annuitant rates differ by about 9% at age 60 [S1] [S7] [derived]; 1.15 sits a little above that and is a standardization.

This table must not be shared with WholeLife_KR_S. One is loaded for survival and the other for death, and using either for both is wrong in a known direction.

Two decrements that pay the same amount, and three columns that are zero#

result_cf() publishes nine columns beside pols_if, and four of them state a product fact rather than carry a number.

claims_death and claims_lapse are the same benefit under two decrements. Both pay db_pp_net(t+1) and cv_pp_net(t+1), which are the same number at every deferral duration on this composite, so the columns differ only in the rate applied and their ratio is exactly (1 − q^m(t)) w^m(t) ÷ q^m(t) — surrenders are taken from the survivors of mortality, so the (1 − q^m) belongs in the identity even though it does not move the displayed figures. At the anchor cell that runs from 50.5 at t = 0 to 3.8 at t = 299 as mortality rises against a lapse rate that steps down, and the two totals come to a ratio of 8.93 over the whole deferral phase. Splitting them is still right: the two are separable the moment a model point carries a 해지공제액, as point 8 does.

commissions is zero in every row and is published anyway. The composite follows a direct-channel product whose published 모집수수료율 is 0.00% in every year [S1]. A zero states the fact; a missing column would only hide it, and would make the reader wonder whether Korean acquisition cost had been forgotten rather than sourced. It is also why the projection’s month 0 is positive at +₩295,841.44 — there is no commission at all, so a single ₩500,000 instalment still covers the whole ₩200,000 cash expense and the month’s decrements, the acquisition charge living inside the fund. On an annual grid the same statement was made against a whole year’s ₩6,000,000 and proved much less.

policy_loans is zero in the base run because loan_on is off, for the reason given under the module table below: the rate is the one parameter that had to be invented.

There is deliberately no claims column. The statement publishes the claims_* split so that its columns sum to net_cf; the claims(t, kind) cells stays, and is what the split columns call. pols_maturity is likewise a count and never a payment — the contract does not mature, it annuitises — but the in-force roll-forward does not close without it on the 확정기간연금형 form, where the survivors of the last instalment neither die nor surrender.

The tax layer is carried and is not a cash flow#

krlib models contractual cash flows. The tax layer is in this model in full because it drives the two behavioural assumptions the product cannot be modelled without — whether the saver persists, and whether the saver annuitises for life — and it is kept out of net_cf because none of it passes through the insurer’s account.

tax_credit_pp(t) is the 세액공제: 15% of contributions where 종합소득금액 is ₩45,000,000 or less and 12% otherwise, on up to ₩6,000,000 a year, grossed up for the 10% 지방소득세 to the 16.5% / 13.2% every consumer document quotes R1 제59조의3제1항 R8 R10 REG-R56. The grossing-up is unverified arithmetic on a verified base: the 지방세법 was not retrieved. It is a credit and not a deduction, so the after-tax value of a contribution falls with income — the opposite of every other market in this repository. At the anchor cell it is ₩990,000 a year, and the anchor premium of ₩6,000,000 sits exactly on the cap. The cap is a per-year figure, so the monthly grid apportions the credit over the year’s twelve months: tax_credit_pp(t) is ₩82,500 a month.
surr_tax_pp(t) is the 16.5% 기타소득세 on a 연금외수령 R3 R5, stated identically by nine carrier documents. One carrier’s surrender illustration carries a 세후지급 예상액 column that is uniformly 83.5% of the surrender value at every duration and on both interest bases [S5] [derived] — exactly 1 − 16.5%.
pension_tax_rate(t) is the withholding on pension income: 5.5% / 4.4% / 3.3% by 만나이, and a flat 3.3% for a 종신계약 from 2026-01-01 R5 R9 R21 REG-R56. That is a dated, quantified 2.2-percentage-point standing advantage to annuitising for life. One caution: 종신계약 is defined by 소득세법 시행령 제187조의2, whose operative text could not be retrieved R7, so whether a guarantee period of any length preserves the status is unverified.
annuity_limit_pp(t) is the 연금수령한도, 평가액 / (11 − 연금수령연차) × 120/100, disapplied from 연금수령연차 11 R6 제40조의2제4항 [S3]. It is a per-year figure too, so check_annuity_limit asserts that no 연금수령연차’s twelve instalments breach it. At the anchor cell it does not bind at all — a contract taken out at 40 could first have drawn at 55, so by 65 the counter has reached 11 — which is exactly why the composite annuitises at 65 and states the constraint for the ages at which it does bite. Model point 6 annuitises at 55, where the first-year limit is 12% of the 평가액.

result_tax() publishes all four beside cv_pp and annuity_pp. Adding any of them to result_cf() breaks check_net_cf() immediately, which is the point of keeping the two frames apart rather than trusting a comment.

Why the lapse assumption is not the savings lapse assumption#

There is no public Korean lapse statistic for 연금저축보험 by policy year. One carrier’s regulatory disclosure carries a 경과기간별 중도해지율 column in which every row reads 「적용안함」 [S13], the supervisor’s comparison table returned a stale quarter [S19], and the behavioural tables of the 2025 whitepaper sit in attachments that did not convert R13. So lapse_table.csv is std and had to be argued from the contract:

a surrender costs 16.5% of essentially the whole payout once the contributions have been credited [S5] [S8] — nothing else in this repository’s savings products has a comparable frictional cost;
netting the credit taken against the charge paid, the saver’s tax cost of surrendering is 16.5% × (환급금 − cumulative contributions) [derived], which is negative while the 환급률 is under 100% and positive after — so the expense friction and the tax friction do not overlap, they hand off, at almost exactly the duration at which the surrender value passes premiums paid;
part of what looks like lapse is 계좌이체 to a 연금저축펀드 or an IRP, which is not a withdrawal and is not taxed [S1], and the market moved that way hard in 2025 — funds +50.7%, insurance −1.2% R13 R22.

The shipped pension vector is therefore materially flatter than a savings vector, and the savings basis is carried beside it so the two can be run side by side; model point 5 uses it, and reaches its annuity date with 0.3831301998 in force against the anchor cell’s 0.6096911403. The supervisory 무·저해지 lapse guidance REG-R27 is not used: it is calibrated to 순수보장성 and 무해지 protection business, and this contract has a full surrender value from the first month and no cliff at 납입완료.

Lapse is absorbing. 부활 and 간편부활 are real, common and specific to this product family — within three years, and the simplified form takes the lapsed months’ charges out of the fund REG-R25 제27조 [S1] [S5] [S7] [S8] — but a premium unpaid at t terminates the contract at t: the 14-day 납입최고 state collapses into the month rather than the year, but it still collapses, and there is no state to re-enter from. So lapse_rate here is a net-of-부활 rate by construction, and a user substituting a gross experience rate will over-decrement. The vector runs through t = n − 1 and is zero from t = n, because surrender is available up to the day before the 연금개시일 [S2] [S4]: month 299 pays ₩81,886.17 of surrender benefit on the full fund, and zeroing the decrement a month early deletes it — where on the annual grid the same slip deleted a whole year’s ₩987,174.98.

Modules that are off in the base run#

Each is a model point column, so a non-anchor point exercises it and the base run stays the worked example.

Column	Off	On at	What it does
`payout_form`	`life_guar`	4, 5, 6	확정기간연금형 over 20 / 10 / 15 years, priced on the declared rate alone
`mort_vintage`	`issue`	7, 9	the 연금개시시점 vintage, and the ratchet
`min_fund_on`	1	9	the 100.1% floor withdrawn, as after a payment holiday
`addl_prem_pp`	0	8	연금저축추가납입특약: 계약관리비용 only, no 계약체결비용
`surr_chg_rate`	0.0	8	the postal insurer’s front-end 해지공제액
`holiday_years`	0	9	납입유예: premiums stop, charges continue, the annuity date defers by `12h` months
`loan_on`	0	9	보험계약대출 at a std rate, drawn on the fifteenth 계약해당일, capped at the surrender value
`par` / `div_rate`	0	9	배당 form: 별표 14 coefficient 4%, dividend applied as an 증액연금
`lapse_basis`	`pension`	5	the savings comparison vector
`rate_scenario`	`base`	6, 8	the guaranteed-rate path, and the 3.5%-for-five-years hybrid

The policy loan rate is the one module parameter that had to be invented, and it is marked as such: no retrieved document gives a numeric 보험계약대출이율 for a 연금저축보험 [S1] [S2] [S4] [S5]. The std 4.00% is set above the only published rate constraint of that kind in the standard conditions, the 평균공시이율 + 1% ceiling on reinstatement interest REG-R25 제27조. That is why the module is off in the base run: switching it on switches on a number nobody published.

Out of scope entirely, each for a stated reason: 계약이전 / 계좌이체 (a wrapper-level movement rather than an insurer cash flow, carried into the lapse rationale instead), 의료비인출 and the six 부득이한 사유 withdrawals and 배우자 승계 (real terms with a real tax effect and no public frequency for any of them), 자유설계연금형 (needs a joint payout state and is offered by three of eight carriers), prospective commutation by a living annuitant (retrieved only on a variable annuity), 납입면제 (「보험료 납입면제 사유 : 없음」 [S5]), and 청약철회 / 품질보증해지 / 고지의무 (pre-inception and rescission machinery — the model begins where cover is in force).

Inputs are external files#

Read once, in `Data`#

Nine CSVs live beside run.py, not inside the model, following annuallife/TradLife_A rather than basiclife/BasicTerm_S’s embedded IOSpec. The model folder holds __init__.py and _system.json and the two Space folders and nothing else, so a diff of the model shows logic changes only, and an input can be swapped without rewriting a formula.

The readers and every *_file Reference live in the unparameterized Data Space, so each file is read once per model rather than once per model point. That is not tidiness: Projection is parameterized by point_id, so every Projection[N] is a separate ItemSpace with its own cells cache, and a reader placed there would re-read all nine files for every policy projected. Data.input_dir() resolves to _model.path.parent at run time and is never hard-coded, which is what lets a licensed or company table drop in as a same-schema CSV with no formula change.

The trade-off, stated in both Space docstrings: the model is not portable on its own. Copying Pension_KR_S/ without its parent’s CSVs produces a model that reads and then fails on first evaluation.

The tables, and why each is std or sourced#

File	Holds	Provenance
`model_point_table.csv`	Nine model points, twenty-one columns, indexed by `point_id`	Configuration. Point 1 is the notes’ anchor cell: its model point is the one the published illustration is struck on [S2], its charge schedule the direct-channel product’s [S1]
`mort_table.csv`	Two annuitant vintages, both sexes, ages 0–120	std Makeham construction on the annuitant basis. Anchored to six published rates [S1] [S7] and calibrated to the factors [S2] implies at two interest bases. Not a copy of any 보험개발원 table — none is public REG-R4 REG-R33 REG-R34
`mort_anchor_table.csv`	The law parameters, the setback, the improvement factor, ω and the six published anchors	Anchors quoted [S1] [S7]; every derived row std. This is the file `check_mort_law` re-derives the shipped rates from
`lapse_table.csv`	Two bases × three segments, annual rates by policy year	std throughout, and argued rather than fitted: no public Korean lapse statistic for this product exists [S13] [S19] R13. The projection applies `lapse_rate_mth`
`decl_rate_table.csv`	Three annual 공시이율 scenarios by policy year	`base` 2.15% is the illustration’s rate [S2]; `floor` is that illustration’s own second column; `hybrid` is one retrieved design [S11]. Adoption std. The projection credits `credit_rate_mth`, the monthly equivalent
`guar_rate_table.csv`	The 최저보증이율 ladder	[S1] [S2] [S13]; the requirement to set one at all is 감독규정 제7-60조제10호 REG-R16
`pricing_table.csv`	Charges, frequencies, 별표 14 coefficients, module parameters	[S1] [S7] for the charges, REG-R20 R14 for the cap coefficients, std for `mort_be_factor` and the loan and holiday parameters
`expense_table.csv`	Best-estimate cash expenses and commission	[std, new here] for the cash levels; the two commission rows are [S1], published as 0.00% in every year
`tax_table.csv`	세액공제, 기타소득세, 연금소득세, the 연금수령 test	R1 R3 R5 R6 R8 R9 R11 REG-R56; the grossing-up for 지방소득세 is unverified arithmetic

Every file but model_point_table.csv carries a provenance column, and every cell in it begins with a citation tag or the word [std]. That is the library’s rule and, here, a necessity: when every row of the mortality file is a standardization, a populated column says nothing unless it names which authority the row stands on.

The time-like columns, and why none of them moved#

No shipped CSV is keyed by a column literally named t, and every time-like column stays in policy years even though the frame counts months. That is the point of the conversion: the contract and the assumptions are annual, and only the grid underneath them got finer, so a year key is read as t // 12 wherever the model consults one.

File	Column or item	Decision	Why
`decl_rate_table.csv`	`from_year`	unchanged, 0-based years	An elapsed policy-year key, read as `max(y ≤ t // 12)`. Its first value is already `0`, so `hybrid`’s 3.5% “for five years” is `t` = 0…59
`guar_rate_table.csv`	`from_year`	unchanged, 0-based years	The same elapsed key; the ladder steps at `t` = 60 and `t` = 120, which is five and ten completed years
`lapse_table.csv`	`from_year`	unchanged, 0-based years	Elapsed key on the `premium_paying` segment (0, 1, 2, 3, 5, 10), giving the annual rate that `lapse_rate_mth` converts. On `paid_up` and `in_payment` the single `0` row is a placeholder key, not a time at all
`pricing_table.csv`	`acq_charge_years` = 7, `surr_chg_years` = 5	unchanged, a count in years	Durations, not indexes: the charge runs `t < 84`, i.e. policy years 1–7
`pricing_table.csv`	`holiday_start_year` = 8, `loan_draw_year` = 15	unchanged, 0-based years	Points on the contract’s own annual axis, read as `t == 180` / `96 ≤ t < 96 + 12h`
`mort_table.csv`	`age`	unchanged	Keyed by attained 보험나이, reached through `age(t) = x + t // 12`; an age, not a time index. 보험나이 increments on the 계약해당일, so that expression is exact
`model_point_table.csv`	`premium_term_y`, `defer_gap_y`, `payout_term_y`, `guar_term_y`, `holiday_years`	unchanged, counts in years	Elapsed-year lengths, as the contract states them
`model_point_table.csv`	`issue_age`, `annuity_start_age`	unchanged	Ages in 보험나이, not points on the time axis

What changed is proj_len(), which is now 12 * proj_years() — the number of projected months — and the derived month counts prem_end_t() and annuitisation_t(). All of them are derived cells; no input moved.

Sign convention#

net_cf is income positive, the library-wide sign, and the technical notes print the stream the same way round, so there is no liability_cf companion — that absence is a fact about which orientation the notes chose, not an omission. A reader comparing the payout years with a model whose notes print outgo-positive must flip the sign: this model’s payout rows are large negatives.

The identity check_net_cf() asserts, in one line:

net_cf(t) = premiums(t) - claims_annuity(t) - claims_death(t) - claims_lapse(t)
            - expenses(t) - claim_expenses(t) - commissions(t) - policy_loans(t)

for every t in 0 … proj_len() - 1 — that is, the columns result_cf() publishes add up to the net_cf column it publishes beside them, and nothing else (the tax layer above all) is folded in. check_net_cf_resid(t) is the signed residual.

The shape is a positive ₩295,841.44 at t = 0, 240 months of thinning positive margin as surrender outgo grows against a level premium base, sixty thin negative months through the gap totalling −₩6,054,921.77, and then 672 months of pure outgo. Undiscounted the anchor cell sums to −₩66,447,581.54; discounted at the monthly equivalent of the rate the fund itself credits it is +₩3,580,561.01 [derived].

Naming#

The cells names are lifelib’s where lifelib has an analogue and the sister libraries’ where they do not: av_pp and cv_pp from the savings chassis, pols_if_at(t, timing) and av_pp_at(t, timing) for the within-year reads, claims(t, kind) with an uppercase kind, check_* / check_*_resid for the identities, roll_fwd_tol for the tolerance, and mort_rate / lapse_rate / credit_rate for the annual assumptions with _mth companions for the monthly conversions the projection applies — the same pairing the other monthly krlib models use. The full mapping from the notes’ actuarial symbols to the cells names is the table in the Projection docstring, headed Notes symbol. Four Korean concepts needed a decision, and the cross-model naming review settled them:

Concept	Name	Not	Why
공시이율, the declared crediting rate	`decl_rate`	`gongsi_rate`	It is the same quantity `delib` spells `decl_rate` for the laufende Verzinsung; a transliterated name would hide the analogy for no gain
예정이율, the pricing rate	`prem_int_rate`	`yejeong_rate`, and above all not `decl_rate`	Two different rates, one of which appears nowhere in the fund recursion. The retired-name register keeps them apart
해약공제액	`surr_chg_pp`	`surr_charge_pp`	The library’s settled abbreviation; `_pp` because it is per policy
표준해약공제액, the statutory cap	`surr_chg_cap_pp`	—	Named for what it is — a cap on the line above — rather than for 별표 14, so the pair reads as one mechanic

Three further names carry a distinction the notes make in prose. credit_rate is not decl_rate: it is the greater of the declared rate and the floor, and it is what the fund earns. annuity_amount_pp is not annuity_pp: the first is B, struck once at t = n and never recomputed, and the second is the instalment payable in a given year, which is B or zero. And pols_if is not lives_if: inside the 보증지급기간 the obligation is unconditional, so pols_if is flat from t = 300 to 419 while lives_if falls from 0.9657433263 to 0.9252034626, and not one of those deaths moves a won.

Standardizations used#

Every quantitative parameter is either source-tagged in a CSV provenance column or marked [std] there, and every one below is repeated in technical-notes.md at the point it is introduced. The observed range is what the retrieved documents actually bracket; a dash means nothing public brackets it at all.

Parameter	Value	Rationale	Observed range
Makeham `A` / `B` / `c`	5.5583e−04 / 2.3281e−06 / 1.108956	No Korean industry table is published REG-R4 REG-R33 REG-R34, so the model ships a construction plus its recipe, fitted jointly to six published rates [S1] [S7] and to two published annuity bases [S2]	Six rates only: 연금사망률 at 50/60/70 [S1], 개인연금사망률 at 40/60/80 [S7]
Female table	Male law set back 4 years	The whole-year setback closest to the published 65세 기대여명 gap of 3.4 years REG-R33; it does not reproduce it — the model’s gap is 3.66	An independent female fit gives a female annuity larger than the male’s, which no rate card does
`annuitant_revised` vintage	Issue vintage × 0.85	One-step lightening of the order the 제9회 → 제10회 revision produced	That revision cut the monthly annuity on a fixed fund by about 15% R19
Terminal age ω	120	No Korean industry table publishes one REG-R33; the generosity costs ₩170,814 of tail outgo over `t` = 76–80, 0.12% of the annuity total	—
`mort_be_factor`	1.15	A loaded pricing basis on the survival side, so a best-estimate death decrement is heavier, not lighter	The two carriers publishing annuitant rates differ by about 9% at age 60 [S1] [S7]
`lapse_rate`, `pension`	4.0 → 1.0% by duration, 0% from `t = n`	Argued from the 16.5% friction [S5] [S8] and from 계좌이체 counting as termination [S1] R13 R22	None public: 「적용안함」 on every row of the one carrier disclosure that has the column [S13]
`lapse_rate`, `savings`	8.0 → 2.0%	The non-qualified comparison vector, carried so the two can be run side by side	—
Lapse absorbing	No 부활 state	The 14-day 납입최고 collapses into the month; the rate is net-of-부활 by construction	부활 within three years is real and common REG-R25 제27조 [S1] [S5] [S7] [S8]
Cash expenses	₩200,000 acquisition; ₩30,000 p.a. deferral, ₩20,000 p.a. payout; ₩30,000 per death claim; 2% inflation	Entirely separate from the contractual 계약체결비용 / 계약관리비용, which are loadings inside the fund; mixing the two double-counts in one direction and destroys the fund calibration in the other	No carrier publishes a cash expense basis; what is published is the loadings [S1] [S7]
공시이율 adoption	2.15%, level, a step function of policy year	The only rate under which the published fund, the published annuities and the reconstructed factors form one consistent set [S2]; a Korean declared rate is majority-weighted to realised return REG-R18 REG-R24	2.1%–3.0%: 3.01% / 2.82% at 2026-09 [S12], 2.40% at 2026-01 [S1], 2.15% at 2025-12 [S2], 2.3% at 2024-10 [S11]
조정률	Not modelled	A discretionary carrier margin living in an unpublished 사업방법서	—
Annuity-phase charge θ	0.5% of the 연금연액	Adoption std: it is what makes the payout formula reconstruct eight published figures on two bases	0.5% at two carriers [S1] [S7]; a third discloses none and runs about 0.6% the other way [S5]
보험계약대출이율	4.00%, module off	std unverified: set above the 평균공시이율 + 1% reinstatement ceiling, the only published constraint of that kind REG-R25 제27조	No retrieved document gives one for this product [S1] [S2] [S4] [S5]
Loan draw	50% of `cv_pp` on the fifteenth 계약해당일	A single visible drawdown rather than a behavioural rule nothing supports	—
납입유예 start	The eighth 계약해당일	Available after three years on two carriers [S5] [S7]	Up to three spells of one year [S8]
Monthly conversions	`(1 + i)^(1/12) − 1` on the credited rate, `1 − (1 − q)^(1/12)` on each probability; `(f − 1)/(2f)` = 11/24 on the life factor	The contract is 월납, the account accrues monthly REG-R19 and the annuity pays 매월, while the filed assumptions are annual	Twelve compound back exactly, so every 계약해당일 reproduces the annual-step figures this model replaced; the annuity correction is worth 1.91% of `B`
별표 14 주3 reading	Whole-term loading levelled over min(m, 10)	Neither reading is excluded by the text; the model states which it takes	The alternative gives ₩1,486,788.72 against ₩1,421,988.72, 4.56% apart
연금수령한도 평가액	Held at the 연금개시 fund throughout	The statute’s 평가액 is not defined for a converted annuity with no residual account	—
만나이 / 보험나이	Both statutory tests read off `age(t)`, which is 보험나이	The two differ by at most one year, and the anchor cell clears 만 55세 by a decade	Material only where 연금개시나이 sits on 55 — model point 6
세액공제 band	16.5%	A contract does not know its owner’s income; nothing in `net_cf` depends on it	13.2% above ₩45,000,000 R1 R8 R10
Annuitisation election	100% 종신연금형, `g` = 10	The composite’s base election; the certain form runs at points 4, 5 and 6	Menus of 10/20/30년/100세 보증 and 5–30년 certain [S6] [S9] [S10]
Guarantee-period death	Continuation at 100%, no commutation	The unpaid guaranteed instalments are paid to the beneficiary, so the stream is unchanged	Commutation at the 공시이율 is available on every retrieved contract [S1] [S2] [S6]
계약자배당	0.000% declared, machinery retained	No carrier publishes a dividend rate on a 연금저축보험, and 무배당 carries the tighter 별표 14 coefficient (3% against 4%) REG-R20	One carrier publishes a five-year 계약자배당 history with its 기준율 [S7]

Tests#

tests/test_model_conventions_kr.py asserts the house style for every model in the library: the folder layout, the Data / Projection split, the read-once property, the docstring contract including the Notes symbol map, the naming rules and the retired-name register, result_cf()’s column conventions, that every shipped model point projects without NaN at the stated length, that every check_*() returns True on every model point, and that read → write → re-read reproduces the same file set and the same numbers.

tests/test_pension_savings_kr.py asserts what this product owes on top of that. The notes’ worked example is hard-coded there — the annuitisation quantities (av_pp(240) = ₩144,311,957.5668497980, av_pp(300) = ₩160,294,805.5909678042, ä = 23.58191601796395, B = ₩6,763,374.5893046195, the implied factor 23.7004181085 against the published 23.70, surr_chg_cap_pp() = ₩1,421,988.7174578153), the thirteen rows of policy year 1 and the turn into year 2, the fund and surrender value at every quoted month-end, the 환급률 column, the payout rows, the annual-to-monthly conversion round trip, the decrement table and both sets of totals — so that a reviewer can check it against the notes by eye to the precision the notes display.

Every pitfall the notes list earns a test named after it: the account recursion with no survivorship release, the deferral-phase strain that is exactly zero, the best-estimate factor whose sign is the opposite of a death product’s, the decrement order W(t) = (l(t) − D(t))w^m(t), the lapse decrement that runs through t = n − 1, the monthly annuity-due factor and the eight-row reconstruction above, mortality in the 종신연금형 factor and its absence from the 확정기간연금형 one, pols_if flat inside the guarantee while lives_if falls, B struck once, the maintenance charge that outlives the premium, the acquisition charge that stops at seven years, the floor that guarantees the credited rate and not the return, the 예정이율 that is not a crediting rate, the tax layer that is not a cash flow, the 연금수령한도 that is disapplied at 연금수령연차 11, the 표준해약공제액 computed on the 연납순보험료, proj_len() as a count rather than the last index, and the 100.1% floor as a survival guarantee. Each of the ten optional modules is asserted in both positions, off and on.

Nine check_*() cells assert the identities the notes imply, each taking no argument and returning a bool over all t, with the signed per-period residual at check_*_resid(t). All nine return True on all nine shipped model points.

Check	Identity
`check_pols_roll_fwd()`	`l(t) − l(t+1) = pols_death(t) + pols_lapse(t) + pols_maturity(t)`
`check_av_roll_fwd()`	`(AV(t) + NP(t) − C(t))(1 + j_c(t)) = AV(t+1)` over the deferral phase
`check_cv_floor()`	`CV(t) = max(0, AV(t) − SC(t))` — 감독규정 제7-66조제1항제1호 REG-R19
`check_surr_chg_cap()`	`SC(t) ≤ SC_max` at every duration — 별표 14 REG-R20
`check_min_fund()`	`F ≥ 100.1% × cumulative premiums` at `t = n`, where the guarantee is on
`check_annuity_total()`	the guaranteed instalments are level and total `kB`, or `gB` on the life form
`check_annuity_limit()`	no 연금수령연차’s twelve instalments exceed the 연금수령한도 R6 제40조의2제4항
`check_mort_law()`	the shipped rates are still the std construction `mort_anchor_table.csv` states
`check_net_cf()`	the published `result_cf()` columns add up to `net_cf(t)`

python -m pytest tests -q