The Projection Space#

The by-policy projection of the CI_KR_S model.

The Space is parameterized by point_id, so Projection[1] is an ItemSpace projecting model point 1:

>>> Projection[1].result_cf()          # the worked example's anchor cell
>>> Projection.point_id = 3            # or switch the default

t counts policy months, 0-based: t = 0 is the first policy month, month t runs from time t to time t + 1, and the contractual policy year label is ``policy_year(t) = t // 12 + 1``. proj_years() = omega_age() - age_at_entry() + 1 is the number of projected policy years and proj_len() = 12 proj_years() the number of months, the frame’s exclusive end, so the frame is range(proj_len()) and the last projected month is t = proj_len() - 1. There is no maturity date and no 만기보험금; the horizon is the terminal age of the mortality table, every remaining life dies in the last policy year, and nothing is paid there but a death benefit.

Annual assumptions stay annual; only the grid underneath them is monthly. Every rate the sources tabulate — mort_rate(), mort_rate_ci(), ci_rate(), lapse_rate(), lapse_rate_ci(), waiver_rate() — holds the annual figure of the policy year the month falls in, and its _mth companion applies 1 - (1 - q)^(1/12), so that the twelve months of a policy year compound back to exactly that year’s rate. The roll-forward applies the companions and nothing else. The one decrement that is not converted this way is the terminal age, where q = 1 admits no root and the certain death is spread uniformly over the year as 1 / (12 - j); and the one rate that is placed rather than converted is the 90-day 보장개시일, which is a date and now falls where the contract puts it — see ci_wait_factor_mth().

Two clocks, and every cells docstring says which one it is on. The month clock is t above: decrements, policy counts, premiums, claims, expenses, and every row of result_cf(), result_pols() and result_val() are indexed by it, and it runs 0 … proj_len() - 1. The month-end clock is a time-point index running 0 … proj_len(), 0 at issue, and carries the contract’s state — pol_val_pp(), cum_prem_pp(), base_benefit_pp(), surr_chg_pp(), cv_std_pp(), cv_mult(), cv_pp(), cv_pp_ci(), resid_db_pp(), loan_avail_pp(), loan_avail_ci_pp() and pol_loan_draw(). It is already 0-based and does not move with the frame. A 계약해당일 is a month-end d = 12 y. Both are written t; they coincide at the opening of a month, because month t opens at month-end t and closes at month-end t + 1. So a claim or a surrender arising in month t, which is paid at the end of it, is paid the month-end-t + 1 amount, and that + 1 is written out wherever it occurs. V(0) = 0 and SC(0) = SC_max are the issue-instant values of the second clock and are real values, not padding.

A post-CI cohort label s is on that same month-end clock: it is the month-end at which the acceleration was paid, so a life accelerating in month t joins cohort s = t + 1. The first policy year’s reduced claims take the negative labels -(t + 1), which are free precisely because no acceleration can be paid at month-end 0 and no full claim ever carries one. The monthly grid turns the annual model’s single reduced cohort into twelve, each paid off its own 기본보험금.

The age basis

Ages are 보험나이 (boheom nai, insurance age): 만나이 at the 계약일 with a fraction under six months discarded and six months or more rounded up, incrementing on each 계약해당일. It is the contractual age, the index of every Korean rate card, and the basis [S3]’s disclosed 예정위험률 grid is stated on, so age(t) = x + t // 12 steps it on exactly that date and nowhere else, and one table rate holds for the twelve months of a policy year. The one contractual exception — 계약의 무효 for an age outside the permitted range, which is judged on 만나이 — produces no cash flow and is not modelled. This is a 보험나이 model throughout; nothing here is on 만나이, and the two differ by about half a year of ageing on every row.

Input data

Inputs are external files: plain CSVs in the model folder’s parent directory, products/ci_insurance/, read at run time rather than stored inside the model. The model folder therefore holds nothing but formulas. This follows annuallife.TradLife_A; contrast basiclife.BasicTerm_S, which keeps its inputs inside the model.

Each table has a filename Reference and a reader Cells, both on Data, reached here through the data Reference:

Reference	Cells	File
model_point_file	data.model_point_table()	model_point_table.csv
mort_table_file	data.mort_table()	mort_table.csv
ci_incidence_file	data.ci_incidence_table()	ci_incidence_table.csv
lapse_table_file	data.lapse_table()	lapse_table.csv

Naming

Cells names follow lifelib’s basiclife.BasicTerm_S and savings.CashValue_SE wherever those models have an analogue — pols_* for policy counts, plural nouns for cash flows, *_rate for rates, *_pp for per-policy amounts, claims(t, kind) with an uppercase kind string. The technical notes use compact actuarial symbols instead. The mapping is:

Notes symbol	Cells	Meaning
(none)	model_point()	The selected model point row
x	age_at_entry()	가입나이 at issue, 보험나이
x + t//12	age(t)	Attained age in month t
(none)	policy_year(t)	1-based policy year label
omega	omega_age()	Terminal age of the table
T_y	proj_years()	Number of projected years
T	proj_len()	Number of projected months
m	prem_term(), prem_period()	납입기간, in years
12m	prem_period_mths()	납입기간, in months
(none)	prem_end()	Number of years a premium is due
n_CI	ci_cover_end()	Months of CI cover
SA	sum_assured()	보험가입금액
G	premium_pp()	Annual gross premium
G^m	premium_mth_pp()	Monthly gross premium
P^m	prem_net_level_mth_pp()	Monthly net level premium
P	prem_net_level_pp()	12 x the monthly one
i	prem_int_rate	예정이율, per annum
j	prem_int_rate_mth()	Its monthly equivalent
a	accel_rate()	선지급 비율
r = 1 - a	resid_rate()	Residual death fraction
c	resid_floor_mult()	계약자적립금 floor multiple
f	first_year_factor	First-year 감액 factor
k	cv_floor_ratio()	저해지 suppression factor
q(t)	mort_rate(t)	Pre-CI death rate, annual
q^m(t)	mort_rate_mth(t)	Pre-CI death decrement
q’(t)	mort_rate_ci(t)	Post-CI death rate, annual
q’^m(t)	mort_rate_ci_mth(t)	Post-CI death decrement
(table q)	mort_rate_at_age(y)	Table rate at attained age y
(none)	mort_rate_base(t)	Pricing-basis rate, annual
(none)	mort_rate_base_mth(t)	Pricing-basis rate, monthly
q_ci(t)	ci_rate(t)	The CI rate, annual
q_ci^m(t)	ci_rate_mth(t)	The CI decrement
(none)	ci_rate_base(t)	Pricing-basis CI rate
(none)	ci_rate_mth_base(t)	Pricing-basis CI, monthly
(by cause)	ci_rate_at_age(y, cause)	Table rate by cause
(none)	ci_wait_factor_mth(t)	90-day 보장개시일, by month
w(t)	lapse_rate(t)	Pre-CI surrender rate, annual
w^m(t)	lapse_rate_mth(t)	Pre-CI surrender decrement
w’(t)	lapse_rate_ci(t)	Post-CI surrender, annual
w’^m(t)	lapse_rate_ci_mth(t)	Post-CI surrender decrement
(none)	disc_factor()	1 / (1 + i)
v^m	disc_factor_mth()	1 / (1 + j)
A1(t)	epv_resid(t)	EPV of the residual, post-CI
A0(t)	epv_ben(t)	EPV of all benefits, pre-CI
a-double-dot(t)	annuity_due(t)	EPV of 1 p.a. while pre-CI
V(t)	pol_val_pp(t)	계약자적립액 at month-end t
cumprem(t)	cum_prem_pp(t)	Premiums paid by month-end t
B(t)	base_benefit_pp(t)	기본보험금 at month-end t
SC_max	surr_chg_cap_pp()	표준해약공제액
SC(t)	surr_chg_pp(t)	해약공제액 at month-end t
W(t)	cv_std_pp(t)	표준형 twin’s 해약환급금 at t
CV(t)	cv_pp(t)	Payable value at t, pre-CI
CV’(t)	cv_pp_ci(t)	Payable value at t, post-CI
(none)	cv_mult(t)	k or 1, by month-end
a B(s)	accel_benefit_pp(s)	The 선지급 of cohort s
r B(s)	resid_nominal_pp(s)	Nominal residual of cohort s
max(rB, cV)	resid_db_pp(t, s)	Residual death benefit at t
(sum)	resid_db_total_pp(t)	Count x payable residual
(sum)	resid_nom_total_pp(t)	Count x nominal residual
(weighted mean)	resid_db_avg_pp(t)	In-force mean residual, month t
L(t)	loan_pp(t)	보험계약대출 balance at time t
i_L	i_loan	보험계약대출이율, per annum
j_L	i_loan_mth()	Its monthly equivalent
Delta(t)	pol_loan_draw(t)	Draw at month-end t
(available)	loan_avail_pp(t)	Loan limit at t, pre-CI
(available)	loan_avail_ci_pp(t)	Loan limit at t, post-CI
l(t)	pols_if(t)	In force, start of month t
l0(t)	pols_if_pre(t)	In force and pre-CI
l1(t)	pols_if_ci(t)	In force and post-CI
l1(t, s)	pols_if_ci_at(t, s)	Post-CI, by cohort s
(survivorship)	ci_surv(t)	Post-CI survival to month t
lp(t)	pols_if_pay(t)	In force and paying
(waived)	pols_waived(t)	Waived on 장해 50%+
C(t)	pols_ci(t)	CI accelerations in month t
C(t, s)	pols_ci_in(t, s)	Entrants into cohort s
(entrants)	ci_cohort_entrants(s)	Cohort s at its entry month
D(t)	pols_death(t)	Pre-CI deaths in month t
D’(t)	pols_death_ci(t)	Post-CI deaths in month t
S(t)	pols_lapse(t)	Pre-CI surrenders
S’(t)	pols_lapse_ci(t)	Post-CI surrenders
G^m lp(t)	premiums(t)	Premium income
(by kind)	claims(t, kind)	Benefit outgo by kind
ec	claim_expenses(t)	Claim expense
E0, e(t)	expenses(t)	Acquisition and maintenance
c0, c_r	commissions(t)	Commission outgo
CF(t)	net_cf(t)	Net cash flow, income positive

The acceleration, in one paragraph

On the first qualifying event the insurer pays a B(s) at the month-end s that closes the month of the event, the contract does not terminate, the death benefit becomes max(r B(s), c V(k)) at every later month-end k, and the premium stops. The contract’s survival is a regulatory requirement and not a design choice: 감독규정 제7-60조제8호 forbids a contract to be extinguished while the risk it covers remains effective [REG-R16]. The complement is exact — a + r = 1, and check_accel_complement() asserts it cohort by cohort — so the acceleration redistributes one sum assured across two dates and never adds cover.

Two cohorts, and why the post-CI one is indexed by its entry month

pols_if_pre() and pols_if_ci() are the two states, and the second is carried by the month-end at which it accelerated, pols_if_ci_at(); a life accelerating in month t is paid at month-end t + 1 and carries the label s = t + 1. That is not tidiness: the residual a post-CI policy carries was fixed at its own acceleration date, at r times the 기본보험금 then, and the 기본보험금 grows with the account and with the premiums paid. Collapsing the cohorts to one average residual would let a policy that accelerated at duration 3 inherit the larger residual of one that accelerated at duration 40. 「지급사유 발생 당시」 is a date, and on this grid it is a month rather than a policy year.

The negative labels are the first-year 감액 cohorts: a breast-cancer claim in the first policy year, t = 0 … 11, is paid a f B(t + 1) with f = 0.5 and leaves a residual of (1 - a f) B(t + 1), a different amount from the full-benefit cohort formed in the same month. Its label is -(t + 1), which is available precisely because no acceleration can be paid at month-end 0 and no full claim ever carries a negative label. The first two are empty, because no 중대한 암 is covered before the 보장개시일. Where the model point sets first_year_scope to all, the whole of the first policy year’s accelerations go into them, which is the GI-generation design.

The cohort dimension is twelve times longer than the annual grid’s, so the aggregates the cash flow actually needs are carried as their own recursions — pols_if_ci(), resid_nom_total_pp() and resid_db_total_pp() — rather than rebuilt by summing the cohort table in every month. Every post-CI cohort runs the same two decrements, so those aggregates are exact; the cohort loop survives inside resid_db_total_pp() for the months in which the 105% account floor sits between the smallest and the largest nominal residual, which is where a closed form is not available and which is a window of a year or two on every shipped point.

Processing order

Within month t, in this order [std order]: premium, acquisition expense, maintenance expense and commission at the start of the month; then the CI transition; then death among those who did not accelerate; then surrender among those who neither accelerated nor died. A life accelerating in month t receives a B(t + 1) at the end of month t — month-end t + 1 — and joins the post-CI cohort at the start of month t + 1, so it is not exposed to the residual death benefit until the following month. That one-month lag is the monthly grid’s version of what was a one-year lag, and the correction is material: the post-CI cohort is now exposed to its own mortality from the month after the claim rather than from the next 계약해당일, and the post-CI in-force at the twentieth 계약해당일 is 1.1% lower than the annual-step model reported for that reason. The lag is still deliberate and conservative in the right direction: the 장해분류표 defers assessment of a 중대한 뇌졸중 for twelve months after onset [S1 별표3], so a CI claim and the death that may follow it are not simultaneous events on any grid.

One policy value, three surrender values

There is a single V(t) in this model, pol_val_pp(), the 계약자적립액 of the 표준형 twin — the non-marketed comparison contract — at anniversary t. The 해약환급금 is W(t) = max(0, V(t) - SC(t)) and the amount actually payable is a multiplier on it:

cv_pp(t) = k W(t) for a pre-CI policy inside the 납입기간, W(t) after it;
cv_pp_ci(t) = W(t) for a post-CI policy at every duration.

All four are on the month-end clock, so a surrender arising in month t — paid at the end of it — is paid cv_pp(t + 1).

The suppression therefore has two exits, not one: 납입완료 and a CI/LTC 지급사유. The second is contractual — [S2] conditions the suppression on 「CI/LTC보험금 지급사유가 발생하지 않은 경우」 and [S4] on 「「선지급 진단보험금」 지급사유 발생 전 납입기간 동안」 — and it is the CI-specific delta on the chassis, whose cliff is a deterministic function of duration. Here it is at min(m, t_CI), a random date correlated with the product’s own decrement. check_cv_carve_out() asserts the consequence the carve-out exists to produce: a CI claimant is never worse off on surrender than an unaccelerated policyholder at the same duration.

The same carve-out doubles the policy loan at the acceleration date, because the loan is computed off the payable value: compare loan_avail_pp() with loan_avail_ci_pp() at any duration inside the 납입기간.

The pricing basis, and what it deliberately leaves out

pol_val_pp() is a prospective net level premium reserve on the 예정이율 and the shipped tables, solved from epv_ben() and annuity_due() and asserted by check_pol_val_roll_fwd(). Two simplifications are [std] and are stated rather than hidden. The pricing recursion values benefits at SA and the residual at r SA, ignoring both floors on the 기본보험금 and the 105% floor under the residual; pricing the second one in would make V self-referential, since the floor is a multiple of V itself. And the reserve is computed on the pricing decrements, not the best-estimate ones, which is what makes the identity testable at all. The floors are benefit-payment rules and are applied in full in the cash-flow projection, where check_resid_floor() asserts them.

The gross premium is a model point input. On the anchor cell it is sourced: ₩306,740 a month is published for exactly that cell, the model point column carries twelve times it, and premium_mth_pp() divides it back — so the monthly grid collects the published rate itself and no modal loading is invented in either direction. On the other cells it is the annual-step model’s own prem_net_level_pp() grossed up by the loading the anchor implies, times the published 저해지-to-기본환급형 form factor [std]. The relativity that falls out is a check rather than an input: the model prices the 80% form at 1.079 times the 50% form at male 40, against the 1.085 [S4] publishes.

예정위험률 are not a best estimate

mort_be_factor and ci_be_factor are 1.00 on every model point but one, so the base run is a valuation-basis run. [S3]’s rates are 예정위험률 carrying a 안전할증 whose regulatory cap was 30% in the early 2000s, 50% from 2015 and removed in 2017 [R1]; no retrieved source sizes the margin against current Korean insured experience, so any best-estimate basis derived from them is a standardization and model point 9 is where it is exercised.

Modules that are off in the base run

보험계약대출, pol_loan_util at 0, drawn on model point 7 at duration 12 — the 계약해당일 d = 144, inside the 납입기간, so the suppressed base binds and the doubling at a CI event is visible.
The 표준형 lapse basis, lapse_basis at table. The suppressed forms run the 로그-선형 원칙모형 of the IFRS17 주요 계리가정 가이드라인 instead, converging to 0.1% at 납입완료 with a 0.8% post-완납 ultimate [REG-R27]. No separate 완납 surrender spike is imposed: the eightfold step at 납입완료 is produced by the guideline’s own shape.
The all-trigger first-year 감액, first_year_scope at all, on model point 4.
The best-estimate levers, on model point 9, which also carries the 110% residual floor multiple [S3] publishes instead of 105%.

What is not modelled, and is named so that it is not mistaken for absent

중도인출 and 추가납입 are arguments of the 기본보험금 definition [S1 별표1 주7] and are held at zero rather than dropped. 부활 and the 90-day 중대한 암 보장개시일 it restarts, the 예정위험률 revision right that takes effect as a benefit reduction rather than a lapse, the 가지급제도, 감액, 연금전환 (which appears in no retrieved CI 약관) and the multi-pay CI generation are all outside this model. So is any 요구자본: the projection produces gross liability cash flows and leaves the 책임준비금, the IFRS 17 CSM and the K-ICS 장해ㆍ질병위험액 to a layer that consumes them.

Sign convention

net_cf() is income positive — premiums less claims, expenses and commission — which is the notes’ own sign and the library-wide one, so there is no outgo-positive liability_cf companion to publish.

Cells Descriptions#

model_point()[source]#: The selected model point as a Series.

sex()[source]#

The sex of the insured, M or F; the two are rated and tabulated separately.

The sex effect on this product runs in opposite directions on price and on incidence, and a reader must not infer one from the other. Female premium is 0.808-0.872 of male across the published grid [S4], while at age 40 the three headline CI rates sum to 1.10 times the male ones [S3] — the excess being breast and thyroid cancer, which is exactly the exposure that broke the 2002 pricing [R1]. The reconciliation is that the premium is dominated by the death benefit, by old-age CI incidence where the female rates are far below the male ones, and by the savings element, which is sex-neutral.

age_at_entry()[source]#

x: the 가입나이 at issue on 보험나이, 15 to 60.

보험나이 (boheom nai, insurance age) is 만나이 at the 계약일 with a fraction under six months discarded and six months or more rounded up, incrementing on each 계약해당일 [S1 제26조] [REG-R25 제21조]. The 15-60 envelope is invariant across every CI source retrieved [S3] [S4] [R13] and is five years below the whole life chassis’s 15-65 ceiling.

sum_assured()[source]#

SA: the 보험가입금액 at issue, level for life.

The envelope is ₩10,000,000 to ₩200,000,000, and the underwriting cap binds the accelerated exposure rather than the face amount: [S3] publishes 2,000만-1억 5,000만원 on the 50% form against 1,000만-9,000만원 on the 80% form, so 0.5 x 1억5,000만 and 0.8 x 9,000만 are within 4% of each other [S3]. 중도인출 and 추가납입 are held at zero [std], so SA is also the 기본사망보험금 of [S1 별표1 주7].

pols_if_init()[source]#

The number of policies in force at the start of the first projected year.

1 on every shipped model point: these are single-policy cells, as everywhere in this library. It is read from the model point rather than hard-coded so that a user can project a block by scaling one row.

prem_term()[source]#

m: the 납입기간 in years, as entered on the model point.

20년납 on the anchor, which is the term every published Korean CI rate card and every 해약환급금 illustration in the source set is quoted on [S3] [S4], and which puts 납입완료 at attained age 60 — well inside the CI cover period, so the surrender-value step and the acceleration can be observed separately. The menu runs 5 to 30년납 in fives and 55 to 80세납, with 5년납 and 10년납 offered on the 기본환급형 only [S4].

prem_period()[source]#

m: the effective 납입기간, and the duration at which the suppression would end.

Identical to prem_term() on every shipped point; the cells exists because the chassis admits a 종신납 form on which the suppressed period runs for life, and a model reading prem_term directly would silently mis-place the step if one were added.

prem_period_mths()[source]#

12 m: the 납입기간 in months, the unit the monthly grid steps in.

The paying months are t = 0 … prem_period_mths() - 1 and 납입완료 falls at the 계약해당일 d = prem_period_mths(). The 납입기간 itself is a contractual term quoted in years and did not change when the grid did: this cells multiplies it out and is the only place the projection needs the product.

prem_end()[source]#

The number of policy years in which a premium is actually due.

prem_period(), so the paying months are t = 0 … prem_period_mths() - 1 and 납입완료 falls at the 계약해당일 d = prem_period_mths(). Nothing else about the contract stops there: maintenance expense, death cover, CI cover to 100세 and the account value all continue, which is the structural point of a whole-life chassis and the reason a projection truncated at 납입완료 misses the majority of the liability.

premium_pp()[source]#

G: the level annual gross premium per policy, payable in advance in years 0 to m - 1.

Level and guaranteed for the whole of 납입기간, subject only to the statutory 예정위험률 revision right from five years — which, where it bites, is applied by reducing the benefit or the sum assured rather than by raising the premium [S3], so its exercise would show up as benefit erosion and not as a decrement. There is no renewal mechanic on the main contract.

On the anchor cell the value is sourced: ₩306,740 a month is published for 남 40, 80% 선지급형, 17대보장형, 해지환급금이 적은 유형, 1억원, 20년납, 월납, net of the 고액계약할인, and the annual figure is twelve times it [std] — no carrier publishes an annual-mode scale, so the modal discount a real 연납 rate would carry is not applied and the annual premium is slightly overstated [S4]. On the other cells it is this model’s own prem_net_level_pp() grossed up by the 1.2400 loading the anchor implies, times the 저해지-to-기본환급형 form factor of 1.10224 published for one identical cell [S4], with 0.937 for the 무해지 form [std].

premium_mth_pp()[source]#

G^m: the level monthly gross premium, the instalment the projection collects.

premium_pp() / 12, which on the anchor cell returns the published ₩306,740 a month exactly — the figure the model point column was built from as twelve times it [S4]. The annual column survives because a Korean commission scale and a 보험료지수 are written in annual units and commissions() reads it; the monthly grid collects this. No modal loading is applied in either direction [std]: no carrier publishes an annual-mode scale, so the division returns the published monthly rate and invents nothing.

accel_rate()[source]#

a: the 선지급 비율, the fraction of the 기본보험금 the CI benefit pays.

0.80 on the composite, 0.50 as a model point flag; both appear together in every complete 약관 retrieved [S1] [S2] [S3] [S4] [S5] [S6]. Paid once only across the whole trigger set — eight 중대한 질병, four 중대한 수술, 중대한 화상 및 부식 and 장기요양상태 — so ci_rate is a first-event rate and not a sum of marginal incidences [S1 별표1] [R1].

80% is the composite’s choice for three reasons stated in product-spec.md, of which the modelling one is that the residual’s 105%-of-account floor actually binds inside a normal projection on this form: at the anchor cell r SA is ₩20,000,000 and the floor takes over as soon as V(t) passes ₩19,050,000. On the 50% form the same test needs ₩47,600,000 and is reached far later. The 100% 선지급플러스형 is excluded because it is not a pure acceleration: it extinguishes the death benefit and replaces it with a separately funded 유족위로금 [S4].

resid_rate()[source]#

r = 1 - a: the residual death fraction, the exact complement of the acceleration.

80 + 20 = 100 and 40 + 60 = 100 exactly [S1] [S2]. The acceleration never adds cover, and keeping r as the arithmetic complement rather than as a second model point column is what makes that unfalsifiable here; check_accel_complement() asserts it against the 기본보험금 cohort by cohort.

resid_floor_mult()[source]#

c: the 계약자적립금 multiple flooring the post-CI death benefit.

1.05 at [S1 별표1 주8], 1.10 at [S3]’s older universal version of the same product, so it is a carrier and vintage parameter and is carried as one rather than hard-coded. The clause reads 「CI/LTC보험금 지급사유 발생당시의 기본보험금의 20%와 … 계약자적립금의 105% 중 큰 금액」, which is why the residual is a growing quantity and not the stated complement: on a long-surviving post-CI policy the account overtakes the nominal and the floor becomes the benefit.

cv_floor_ratio()[source]#

k: the 저해지환급형 suppression factor applied to the 표준형 twin’s 해약환급금.

1.00 표준형 / 기본환급형, 0.50 저해지환급형, 0.00 무해지환급형. [S2] states both grades it offers in terms — 「’30% 저해지환급형’의 경우 ‘기본형’ 해지환급금의 30%… ‘50% 저해지환급형’의 경우 … 50%」 — and 0.50 is taken because it is the modal fraction on the chassis and one of the two grades this carrier offers on the CI product itself [std]. [S4] rebrands the same mechanic as 해지환급금이 적은 유형 and prices it 9-12% below the 기본환급형.

The suppression is a regulatory dispensation rather than a contractual gimmick: 감독규정 제7-66조제4항 permits an insurer to pay less than the 별표-14 floor only where the premium was calculated on a 최적해지율, which is why the lapse assumption on this product is a supervisory matter [REG-R19] [REG-R27].

first_year_scope()[source]#

The scope of the first-year 감액: breast (the composite) or all.

Two designs are in the sources and they differ in scope, not in depth — both halve. [S1] and [S2] reduce only for breast cancer and only in the first policy year, so an 80% form pays 40% and the death benefit’s complement rises to 60% [S1 별표1] [S2 별표1]. [S4]’s GI product halves every trigger in the first year, carving back only a 중대한 화상 및 부식 claim on the 17대보장형 [S4].

The composite takes the breast-cancer design because it is the CI-generation design in both complete 약관 retrieved and because it is the only one with an identifiable experience rationale: it is the lineal descendant of the 180-day breast-cancer 부담보 imposed across the market from 2008 after the female claim excess of 2003-2005 [R1]. The modelling consequence is real — it requires the 중대한 암 incidence to be split into a breast component and the rest, which breast_share() supplies.

breast_share()[source]#

The share of 중대한 암 incidence attributable to breast cancer [std].

0.268 for females and 0.005 for males, calibrated on the national cancer registry [REG-R40]: 유방 29,871 cases in 2023 against female cases of 137,487 less the 19.0% of the female burden that is 갑상선, which 중대한 암 excludes as C73 — so 29,871 / 111,364 = 0.268. Male breast cancer is under 1% of breast cases and is carried at 0.005 rather than nil so that the male first-year 감액 is present and negligible rather than absent and unexplained.

The registry publishes incidence on 만나이 while this model runs on 보험나이; the quantity used here is a share of one age’s incidence, which is first-order insensitive to the half-year shift, and no adjustment is made [std].

lapse_basis()[source]#

The surrender basis: log_linear (the 원칙모형) or table (the 표준형 curve).

The IFRS17 주요 계리가정 가이드라인 of 2024-11-07 adopts a 로그-선형 모형 as the 원칙모형 for 무·저해지 lapse rates, converging to 0.1% at 납입완료 with a 0.8% post-완납 ultimate; departure is permitted only on disclosure, against the principle model, of the CSM, best-estimate liability, K-ICS and net-income differences [REG-R27] [R3]. The suppressed model points run it; the 기본환급형 points run the 표준형 duration curve in lapse_table.csv. Carrying both is the comparison the guideline requires an insurer to disclose, and it is the reason the table survives on a product whose representative form does not use it.

The problem the supervisor named bites here with particular force: with no experience on 무·저해지 business, insurers assumed high lapse right up to 완납, which flatters profitability, and the resulting switching raised observed 표준형 lapse, which was fed back into the 무해지 assumption — 「악순환」 [REG-R27].

mort_be_factor()[source]#

The multiplier turning the shipped valuation mortality into the projection basis.

1.00 on every model point but 9, so the base run is a valuation-basis run and not a best estimate: [S3]’s rates are 예정위험률 carrying a 안전할증 whose regulatory cap was 30% in the early 2000s, 50% from the 2015 로드맵 and removed from 2017, and no retrieved source sizes the margin against current Korean insured experience [R1]. Claims move proportionately with it; the terminal rate is held at 1 whatever it is set to, because omega_age is the horizon of the table and a structural property of the projection rather than an experience assumption.

ci_be_factor()[source]#

The same lever on the CI decrement; 1.00 on every model point but 9 [std].

Held apart from mort_be_factor() because the two margins are not the same size and there is no reason to move them together: the mortality basis is a life table and the CI basis is a morbidity table built on six disclosed numbers, and the second is by far the weaker of the two. 0.75 on model point 9, removing a quarter of the rate as a stated [std] unwinding of the 안전할증 [R1].

mort_ci_factor()[source]#

The multiplier on mortality after a CI event [std]; 3.00 in the base run.

The CI and death decrements are not independent competing risks, and the product is built on the fact that they are not. There is no survival period anywhere in a Korean CI contract — the supervisor refused the overseas 30-day requirement on consumer-protection grounds, holding that requiring survival would create disputes where the insured died [R1] — so the CI rate already includes lives who die of the CI cause, and a fraction of what would be a death claim on an ordinary 종신보험 is a CI claim here followed shortly by a residual death claim.

No Korean post-CI mortality is published. 3.00 is a standardization whose rationale is the registry’s own survival data: five-year relative survival across all cancers excluding thyroid is 69.6% against a general population at 100% by construction [REG-R40], and the CI trigger set is deliberately the severe tail of each disease. It is a model point column so that the sensitivity can be read directly, and model point 9 runs it at 2.00.

waiver_rate(t)[source]#

The annual 납입면제 rate on the 장해 50%+ limb alone [std].

[S1] waives all future 기본보험료 on either a 장해지급률 of 50% or more from one accident or one non-accidental cause, or any CI/LTC 지급사유 [S1 별표1 주4]. Because the second limb fires with essentially every CI claim, the waiver is not an independent decrement on the CI limb and is not modelled as one: it is implicit in the post-CI cohort, which pays no premium at all. What is left is the first limb, a real if second-order decrement on the same 장해분류표 percentage scale the chassis uses [REG-R25].

0.03% a year during the 납입기간 on every shipped point but 9, which runs 0.05% [std]; no Korean disability inception rate at the 50% 장해지급률 threshold is published. A waived policy stays pre-CI, keeps its full death cover and — the chassis’s “waived premiums count as paid” rule — continues to accrue surrender value on the full premium scale, so the waiver is the only route to the 저해지 step without funding it. Zero once no premium is due, that is from t = prem_period_mths(). Its monthly companion is waiver_rate_mth().

pol_loan_util()[source]#

The fraction of the available 보험계약대출 drawn; 0 in the base run [std].

There is no public Korean take-up data of any kind, so the level is a model point input and the contractual limit in loan_avail_pp() binds it whatever it is set to. Model point 7 draws half the available amount at duration 12, inside the 납입기간, where the base is the suppressed value — which is the configuration in which the CI carve-out’s doubling of the limit is visible.

pol_loan_year()[source]#

The anniversary at which the 보험계약대출 is drawn; 0 for no draw.

An elapsed count of completed policy years — duration 12 on model point 7 — and so already 0-based: it is a point on the anniversary clock, not an index into the frame, and it did not move when the frame did.

omega_age()[source]#

omega: the terminal age of the mortality table, the first age at which q = 1.

110 on the shipped construction, for both sexes [std]. The 제10회 경험생명표’s terminal age is not published — 보험개발원 releases only 평균수명 and 기대여명 [REG-R33] [REG-R34] — so the horizon is a stated property of the constructed table and not a transcription. It is a hard model parameter and not a rounding: projecting a whole-life contract to 100 truncates the liability and projecting to 120 invents one.

proj_years()[source]#

T_y = omega - x + 1: the number of projected policy years.

The contract’s own clock. The projection steps in months and carries 12 T_y of them; this cells is what every quantity quoted in policy years — the 납입기간, the 해약공제기간, the CI cover period — is measured against.

proj_len()[source]#

T = 12 T_y: the number of projected policy months.

The frame’s exclusive end, not its last index: result_cf() carries proj_len() rows indexed 0 … proj_len() - 1 and the frame is range(proj_len()), twelve rows to a policy year.

There is no maturity date and no 만기보험금, so the horizon is the table’s and not the contract’s. Every remaining life dies in the last policy year — the table’s rate is 1 there and mort_rate_mth() spreads that certain death evenly over its twelve months — and pols_if(T) is zero; there are no tail states. CI cover ends earlier, at the 100세 계약해당일 — see ci_cover_end() — so the projection carries a long stretch on which the death benefit is the only cover left.

policy_year(t)[source]#

The contractual, 1-based policy year label of month t: t // 12 + 1.

Derived and never indexed by. The 계약해당일 closing policy year y is the month-end d = 12 y, and everything the contract quotes in policy years — the 납입기간, the 해약공제기간, the lapse table’s rows, the CI cover period — is read through this.

age(t)[source]#

x + t // 12: the attained 보험나이 in month t, which is 0-based.

보험나이 increments on the 계약해당일 and not on the birthday [REG-R25 제21조], so the floor division is exact rather than an approximation: one table rate holds for the twelve months of a policy year, which is what the contract says.

ci_cover_end()[source]#

n_CI: the number of policy months in which the CI benefit is covered.

The death benefit is 종신 but CI/LTC cover ends at the 100세 계약해당일, so the last covered month is t = n_CI - 1 and n_CI = 12 (100 - x). This is the post-2008 design and is the one a contract written today has: the 2002 product put the acceleration inside a 제1보험기간 running to the 80세 계약해당일 and paid 100% of the death benefit thereafter [S6] [R1], and that legacy split is named in product-spec.md and deliberately not modelled, because a second discontinuity at 80 would collide with the 저해지 step in any model point trying to isolate either.

mort_rate_at_age(y)[source]#

The shipped table’s mortality rate at attained age y, before any adjustment.

Read from mort_table.csv, a [std] construction anchored on the 예정 경험 사망률 one Korean CI 상품요약서 discloses at ages 20, 40 and 60 [S3]; see Data. This is the rate the pricing recursions use unadjusted: mort_be_factor is a lever on the decrement, not a change to the 산출방법서 basis.

mort_rate_base(t)[source]#

The annual pricing-basis mortality rate in month t, at attained age age(t).

One table rate holds for the twelve months of a policy year, because 보험나이 steps on the 계약해당일.

mort_rate_base_mth(t)[source]#

The monthly pricing-basis mortality rate in month t.

1 - (1 - q)^(1/12) on mort_rate_base(), so twelve months compound back to exactly the year’s tabulated rate, and 1 / (12 - t mod 12) in the terminal policy year where q = 1 — see mort_rate_mth() for why.

mort_rate(t)[source]#

q(t): the annual death rate of the pre-CI cohort in the policy year of t.

The table rate times mort_be_factor(), capped at 1 and held at 1 at the table’s terminal age whatever the factor is set to. This is the rate the sources tabulate; what the roll-forward applies is mort_rate_mth().

mort_rate_mth(t)[source]#

q^m(t): the death decrement applied to the pre-CI cohort in month t.

1 - (1 - q(t))^(1/12) [std], the uniform-force conversion, so that the twelve months of a policy year compound back to exactly the annual rate the table holds. Dividing by twelve would not, and on a rate that rises by two orders of magnitude across the horizon the difference is not a rounding.

At the table’s terminal age q = 1 and no compounding is available: the conversion would kill the whole surviving cohort in the first month and leave eleven empty rows. The certain death is therefore spread uniformly over the year as 1 / (12 - j) in its j-th month, which is the UDD convention and closes the table exactly.

mort_rate_ci_base(t)[source]#

The annual pricing-basis mortality of a post-CI life in the policy year of t.

The table rate times mort_ci_factor(). It is what epv_resid() values the residual on, so the reserve carries the same excess mortality the projection does; a pricing basis that valued the residual on ordinary mortality would hold too little against it.

mort_rate_ci_base_mth(t)[source]#

The monthly pricing-basis mortality of a post-CI life in month t.

1 - (1 - q')^(1/12), and the terminal-year UDD spread of mort_rate_mth().

mort_rate_ci(t)[source]#

q’(t): the annual death rate of the post-CI cohort in the policy year of t.

mort_rate() times mort_ci_factor(), capped at 1. The post-CI cohort is the only place in this model where the correlation between the two decrements appears as a number, and it is the reason the residual death benefit is paid earlier than an ordinary 종신보험’s would be.

mort_rate_ci_mth(t)[source]#

q’^m(t): the death decrement applied to the post-CI cohort in month t.

1 - (1 - q'(t))^(1/12) [std], with the terminal-year UDD spread of mort_rate_mth(). The excess mortality is applied to the annual probability and then converted, not to the converted one: a factor of three on a monthly force is not a factor of three on the year, and the 3.00 that stands behind this number is a statement about a year’s survival [REG-R40].

ci_rate_at_age(y, cause)[source]#

The shipped incidence rate at attained age y for one of the five modelled causes.

cancer, ami and stroke are 중대한 암, 중대한 급성심근경색증 and 중대한 뇌졸중, sourced at ages 20, 40 and 60 [S3] and constructed elsewhere; other covers the five remaining 중대한 질병, the four 중대한 수술 and 중대한 화상 및 부식; ltc is 장기요양상태 on 노인장기요양 1·2등급. See Data for what each rests on. Zero above the last tabulated age.

ci_wait_factor()[source]#

The first-year proration for the 90-day 보장개시일 [std].

1 - 90/365 = 0.7534. The 중대한 암 보장개시일 is 「계약일(부활일)부터 그 날을 포함하여 90일이 지난날의 다음날」 [S1 제7조] [S1 별표1 주1] and is invariant across every document retrieved [S1] [S2] [S3] [S4]; 장기요양상태 carries the same 90 days, waived where the state arises directly from a 재해 [S1 별표1 주2]. Everything else — the other seven 중대한 질병, the four 중대한 수술 and 중대한 화상 및 부식 — is covered from the 계약일 with no waiting period at all [S1] [S2 별표1 주1].

1 - 90/365 is the first policy year’s aggregate exposure for the two causes that carry the wait, and it is what the twelve monthly factors of ci_wait_factor_mth() add up to. It is published because it is the number an annual-step model would use for the whole of the first year, and because the two figures agreeing is the check that the monthly placement of the wait did not change its size.

Neither form models the two consumer protections that ride on the wait — the right to cancel and recover the premiums where 중대한 암 is diagnosed before the 보장개시일, and the five-year revival of cover for a pre-inception cancer [S1 제7조⑤⑥].

ci_wait_factor_mth(t)[source]#

The fraction of month t that falls after the 90-day 보장개시일.

clamp(((t + 1) * 365/12 - 90) / (365/12), 0, 1) on a mean month of 365/12 days: zero in months 0 and 1, 0.0411 in month 2, and 1 from month 3 on. That is the substantive gain of the monthly grid on this decrement — the 보장개시일 is a date, 「계약일(부활일)부터 그 날을 포함하여 90일이 지난날의 다음날」 [S1 제7조] [S1 별표1 주1], and an annual grid could only smear it across the whole first year as a 0.7534 proration on the assumption that incidence is uniform within it. The monthly grid puts the cover where the contract puts it: none for the first two months, a twenty-fifth of the third, and all of it thereafter.

The twelve factors sum to 12 * (1 - 90/365) = 9.0411 months of exposure, so the first policy year carries exactly the 275 days of cover the contract gives it and the conversion moves the wait without resizing it. The wait is invariant across every document retrieved [S1] [S2] [S3] [S4]; 장기요양상태 carries the same 90 days, waived where the state arises directly from a 재해 [S1 별표1 주2]. Everything else — the other seven 중대한 질병, the four 중대한 수술 and 중대한 화상 및 부식 — is covered from the 계약일 with no waiting period at all [S1] [S2 별표1 주1], so this factor is applied to the 중대한 암 and 장기요양 limbs only.

ci_wait_share(t)[source]#

The share of the month’s tabulated CI incidence that carries the 90-day wait.

(cancer + ltc) / total at the attained age of month t — the two causes whose 보장개시일 is 90 days after the 계약일 [S1 별표1 주1] [S1 별표1 주2], over the five-cause first-event total. Used only to apply ci_wait_factor_mth() to the part of the decrement it belongs to; zero where there is no cover at all.

ci_rate_base(t)[source]#

The annual pricing-basis CI decrement of the policy year of month t.

The five causes summed at the attained age, capped at 1, and zero from t = ci_cover_end(). This is the rate the source tabulates, before the 90-day 보장개시일 is applied: the wait is a date inside the first policy year and belongs to the monthly rate, ci_rate_mth_base(), and not to the year’s tabulated figure. Summing is legitimate here only because the shipped rates are themselves first-event rates across the competing-risk set: the benefit is payable once only across every trigger [S1 별표1], and Korea’s supervisor required the overlap between CI causes to be reflected in the filed rate rather than ignored for rate stability as overseas practice does — 「CI 질병들 간 중복해서 발생할 수 있는 확률을 최대한 반영한 최종 위험률로 검증받고 사용하였다」 [R1]. A table built by adding published site-specific incidences would be wrong in exactly the direction the regulation addresses.

ci_rate_mth_base(t)[source]#

The monthly pricing-basis CI decrement in month t, wait applied where it falls.

[1 - (1 - q_ci)^(1/12)] on the year’s first-event total, so twelve months compound back to exactly the tabulated annual rate, times the month’s cover factor

1 - (1 - ci_wait_factor_mth(t)) * ci_wait_share(t)

which removes the 중대한 암 and 장기요양 limbs from the two months the 보장개시일 has not yet passed and 96% of them from the third. Everything else is covered from the 계약일 and is never withheld.

Converting the summed first-event rate rather than each cause separately is the same choice the annual rate makes and for the same reason: the benefit is payable once only across the whole trigger set [S1 별표1] and the filed rate already carries the overlap between causes [R1].

ci_rate(t)[source]#

q_ci(t): the annual CI rate of the policy year of month t.

ci_rate_base() times ci_be_factor(), capped at 1. Morbidity dominates mortality on this chassis: on [S3]’s own disclosure the three headline rates sum to 3.70 times the death rate at male 40 and 6.70 times it at male 60, which is why a projection of this product is a morbidity projection with a mortality tail rather than the reverse, and why the CI benefit takes about half the risk premium at a 50% acceleration despite paying only half the sum assured [S3].

ci_rate_mth(t)[source]#

q_ci^m(t): the CI decrement applied in month t.

ci_rate_mth_base() times ci_be_factor(), capped at 1. It is zero in the first two months of the contract for the 중대한 암 and 장기요양 limbs and positive for the rest from the 계약일, which is what the 약관 says and what an annual grid cannot express.

ci_reduced_share(t)[source]#

The share of month t’s CI claims paid at the reduced first-year rate.

Zero in every month but the twelve of the first policy year, t = 0 … 11 — the 감액 runs for a policy year and not for a projection step, so the monthly grid carries it over twelve rows where the annual grid carried it over one. Inside that year it is 1 where first_year_scope is all, and otherwise the breast-cancer share of that month’s own CI decrement — breast_share() times the 중대한 암 component after the month’s 보장개시일 factor, over ci_rate_mth_base(). So it is zero in the first two months, where no 중대한 암 is covered at all, and the reduced cohorts formed there are empty.

Splitting the decrement rather than averaging the benefit is what lets the two kinds of first-year cohort carry different residuals, which they must: a reduced claim leaves (1 - a f) B(d) and a full one leaves r B(d), both at the month-end d the claim is paid at.

lapse_rate_base(t)[source]#

The annual 표준형 surrender rate of the policy year of month t, from the table.

The file is keyed by the contractual, 1-based ``policy_year`` label, so month t is read at row policy_year(t) and the file itself is untouched by the grid; rows past the last are the level tail. A published 해지율 is an annual figure and stays one: the conversion to a month happens in lapse_rate_mth() and nowhere else.

9% / 7% / 5.5% / 4.5% / 3.8% / 3.2% and a 2.8% tail, all [std]. No CI lapse experience of any kind was retrieved — [R1] gives one cession ratio and no lapse data at all — so the curve is bounded rather than fitted: Korean 상품요약서 publish the 적용해지율 used in pricing in envelope form, and one carrier’s protection product discloses 0%-13.4% during the payment period against 1%-10% at another. The tail sits far above the 0.8% post-완납 ultimate the supervisor’s 원칙모형 sets, and that gap is the subject of [REG-R27].

lapse_rate_ult()[source]#

The post-납입완료 ultimate surrender rate of whichever basis is in force.

0.8% on the 로그-선형 원칙모형, which the IFRS17 주요 계리가정 가이드라인 sets as the post-완납 rate for 무·저해지 business [REG-R27]; the table’s own tail otherwise, read at the first month after 납입완료. Annual, like everything in the table.

lapse_rate(t)[source]#

w(t): the annual surrender rate of the pre-CI cohort in the policy year of t.

This is the rate the sources tabulate and the supervisor sets; its monthly companion is lapse_rate_mth(), and the pair is the library-wide convention on every monthly model. On the log_linear basis it is the guideline’s 원칙모형 — geometric decay from a first-year 10% [std] in policy year 1 to the 0.1% the guideline sets at 납입완료, reached in the last paying year, then the 0.8% post-완납 ultimate from t = 12m [REG-R27]. On the table basis it is lapse_rate_base() unchanged. The decay runs on the policy year and not on the month, so the rate is level across the twelve rows of a policy year, which is how the guideline states it.

No separate 완납 surrender spike is imposed. The eightfold step from 0.1% to 0.8% at 납입완료 is produced by the guideline’s own shape, and the contractual step in cv_pp() that provokes a real surge is a different object from the behavioural assumption about it; conflating the two is how a spike gets counted twice.

A surrender is not a pure decrement here: it pays cv_pp() net of any loan, and that value is suppressed during the 납입기간, which is precisely why early surrender on this form is assumed low.

lapse_rate_mth(t)[source]#

w^m(t): the surrender decrement applied to the pre-CI cohort in month t.

1 - (1 - w(t))^(1/12) [std], so that the twelve months of a policy year compound back to exactly the annual rate the table or the guideline states. On the log_linear basis the vector spans two orders of magnitude — 10% to 0.1% — and dividing by twelve instead of compounding would understate the early months by 4.9% of the rate and overstate the late ones; only the compounding convention reproduces the supervisor’s own annual figure at every 계약해당일.

lapse_rate_ci(t)[source]#

w’(t): the annual voluntary surrender rate of the post-CI cohort.

The ultimate rate of the basis in force times lapse_ci_factor [std], level in t. A post-CI policy is premium-waived, so it is in the paid-up state by construction and the paying-period curve does not describe it whichever basis is chosen.

The factor is 0.50 and its direction is genuinely ambiguous, which is why it is a lever rather than a finding. A CI claimant has no premium to fund and may value the residual cover highly, which argues for less surrender; but the carve-out has just doubled the cash available, which argues for more. Nothing in any retrieved document bears on it.

lapse_rate_ci_mth(t)[source]#

w’^m(t): the surrender decrement applied to the post-CI cohort in month t.

1 - (1 - w'(t))^(1/12), level in t like the annual rate it converts.

waiver_rate_mth(t)[source]#

u^m(t): the 장해 50%+ 납입면제 incidence applied in month t.

1 - (1 - u(t))^(1/12) on waiver_rate(), so twelve compound back to the annual figure the model point carries. The monthly grid also puts the transition in the month of the 장해 rather than at the next 계약해당일, which is when the 약관 stops the premium.

prem_int_rate_mth()[source]#

j: the monthly equivalent of the 예정이율, (1 + i)^(1/12) - 1.

Twelve of these compound back to exactly 1 + i, so the pricing basis is the same basis the annual-step model used and only the step changed.

i_loan_mth()[source]#

j_L: the monthly equivalent of the 보험계약대출이율, (1 + i_L)^(1/12) - 1.

The 약관 quotes 보험계약대출이율 as an annual rate — 예정이율 + 1.5% = 4.00% on this chassis — so the monthly roll runs on its twelfth root and twelve months compound back to exactly the quoted figure.

disc_factor_mth()[source]#

v^m = 1 / (1 + j): the monthly discount factor of the 예정이율.

What every EPV in this model discounts on, the pricing recursions having moved to the month with the projection. disc_factor() survives beside it as the annual figure the 예정이율 is quoted as.

disc_factor()[source]#

v = 1 / (1 + i): the annual discount factor of the 예정이율.

2.50% flat, inherited unchanged from the whole life chassis and [std]. No CI-specific pricing rate later than 2011 was retrieved and the two that exist bracket it from too far away to be useful — 연복리 4.0% on a January 2011 CI product [S3] and about 2.75% on a 2019 종신 illustration basis [S4] — while the chassis reads six values off 2021-2025 carrier documents spanning 2.25%-2.75% and takes the mid-point, which is also the 2026 평균공시이율 [REG-R48]. A library whose CI product and whose whole-life product discounted on different rates would make the cost of the acceleration impossible to read off the difference between them.

Note that 예정이율 is not a regulatory term in Korea: a full-text search of the 감독규정 returns no occurrence, and the regulation speaks only of the 계약자적립액 적용이율 and of the 금리연동형 / 금리확정형 distinction [REG-R9] [REG-R48]. Interest matters less here than on the chassis, because a CI benefit is paid a decade or more before the death benefit it accelerates and the liability is correspondingly shorter.

epv_resid(t)[source]#

A1(t): the EPV at the start of month t of the residual, for a post-CI life.

v^m [q'^m r SA + (1 - q'^m) A1(t + 1)] on the pricing basis, with A1(T) = 0. It values the residual at its nominal r SA and ignores the 105% account floor [std]: the floor is a multiple of V and V is built out of this quantity, so pricing it in would make the reserve self-referential. The projection applies the floor in full, and check_resid_floor() asserts it there.

epv_ben(t)[source]#

A0(t): the EPV at the start of month t of every future benefit, pre-CI.

The two-state recursion this whole product reduces to, a month at a time:

A0(t) = v^m [ q_ci^m a SA + (1 - q_ci^m) q^m SA
              + q_ci^m A1(t + 1) + (1 - q_ci^m)(1 - q^m) A0(t + 1) ]

The acceleration is a timing effect and nothing else. Because a + r = 1 exactly, a life that accelerates and then dies pays the same total as a life that simply dies; the CI event moves a SA of it forward by the years between the two events. At the anchor cell that is worth 24.4% of the net premium against the same contract with no acceleration, and it is the whole actuarial content of the product.

A0(T) = 0 is the base case, at T = proj_len().

annuity_due(t)[source]#

The EPV at the start of month t of 1 a month while pre-CI and premium due.

1 + v^m (1 - q_ci^m)(1 - q^m) a(t + 1) for t < 12m, zero from t = 12m, so it is measured in months of premium and A0 / a is a monthly net premium. The CI decrement is in the annuity as well as in the benefit, because any CI/LTC 지급사유 waives all future 기본보험료 [S1 별표1 주4]: a premium stream that ran on through the post-CI state would over-fund the contract by the whole of the waiver.

prem_net_level_mth_pp()[source]#

P^m: the monthly net level premium on the pricing basis, A0(0) / a(0).

The quantity the account is built out of, and the one the monthly equivalence P^m a^m(0) = A0^m(0) solves for. A pricing quantity that never becomes a cash flow: what is collected is premium_mth_pp().

prem_net_level_pp()[source]#

P: the annualised net level premium, 12 P^m.

Published so that the loading can be read against the annual gross the model point carries: on the anchor it is ₩3,051,133.35 against a gross of ₩3,680,880, a loading of 20.6% — which sits close to, and is a different quantity from, the 보험료지수 of 130.1% [S3] publishes for the same form, that ratio being against the 표준순보험료 computed on the supervisor’s prescribed rates rather than on this model’s. Both sides of that ratio are twelve times a monthly figure, so the comparison is the like-for-like one.

It is 2.78% above the annual-equivalence premium the annual-step model solved for, and that is the ordinary modal effect of paying monthly in advance rather than once a year: eleven of the twelve instalments arrive later and are exposed to the year’s decrements before they do. The model point file’s own premiums were derived from the annual-step figure and are unchanged — they are inputs, not outputs — so the loading the anchor now implies is 20.6% where it was 24.0%.

It is not an annual-equivalence premium and is not used as one: nothing in the model solves P a(0) = A0(0) on an annual grid any more. Nor is it the 연납순보험료 that enters the 표준해약공제액; that is surr_chg_cap_pp(), which follows the chassis in taking 80% of the gross premium [std] so that the statutory cap can be reproduced from published quantities alone.

pol_val_pp(t)[source]#

V(t): the 계약자적립액 at month-end t, prospective and net level premium.

On the month-end clock: t = 0 is the issue instant and t = T the horizon, so this cells is defined for t = 0 … proj_len() and does not move with the frame. The account that month t opens with is V(t) and the one it closes with is V(t + 1). A 계약해당일 is t = 12 y.

A0(t) - P^m a(t), zero at t = 0 — by the definition of P^m — and at t = T. It is the account of the 표준형 twin — the non-marketed comparison contract priced with the lapse assumption switched off — and there is exactly one of it in this model: the suppression is a haircut on this value, the post-CI carve-out lifts the haircut off this value, and the 기본보험금 and residual floors read off this value. CV(t) is therefore independent of the sold form’s own premium, which is the whole of the 환급률 arithmetic that sells the 저해지 form.

The recursion it satisfies is asserted by check_pol_val_roll_fwd(). [S3] words the same identity in a CI product’s own terms — 「보험료 계산시 적용한 위험률로 산출한 순보험료식 책임준비금에서 미상각신계약비(해지공제액)를 공제한 금액을 해지환급금으로 지급합니다」 — and [S1]’s 약관 sends the calculation to the 산출방법서, which is filed and unpublished [REG-R2].

cum_prem_pp(t)[source]#

cumprem(t): gross premiums paid per policy by month-end t.

G^m min(t, 12m), the instalments falling at the month-ends 0 … 12m - 1. This is one of the three limbs of the 기본보험금, and the monthly grid is what makes it a true running total: 이미 납입한 보험료 grows twelve times a year, not once. Waived premiums count as paid — the chassis’s rule, carried over — so a policy on the 장해 50%+ waiver reaches the same cumulative figure without funding it.

base_benefit_pp(t)[source]#

B(t): the 기본보험금 at month-end t, the base every percentage applies to.

On the month-end clock, so a claim arising in month t — paid at the end of it — is paid off B(t + 1).

max(기본사망보험금, 이미 납입한 보험료, c V(t)) with 기본사망보험금 = 보험가입금액 - 중도인출금액 + 추가납입보험료 [S1 별표1 주7], the last two held at zero [std] — named rather than dropped, because a model that ignores them must say it holds them at zero rather than silently leaving them out of the definition.

At the anchor cell neither floor binds within the 납입기간, and it is worth saying so plainly so that the model is not read as being built around a clause that never fires: cumulative premiums at 납입완료 are ₩73,617,600 against a face of ₩100,000,000, and c V(t) reaches the face only when V passes ₩95,238,095. The floors bind where a Korean designer would want them to — a short-pay or high-premium cell, and a very old attained age. The floor on the residual is a different matter and binds early: see resid_db_pp().

The premiums-paid limb is the contractual form of a supervisory design rule, 감독규정 제7-60조제9호, which requires the death benefit to be at least cumulative premiums paid except where the payment period ends at age 80 or below [REG-R16] — and on the anchor cell 납입완료 falls at attained age 60, so the exception applies and the rule does not strictly bite.

surr_chg_cap_pp()[source]#

SC_max: the statutory 표준해약공제액, the cap on the surrender charge.

연납순보험료 x 5% x 해약공제계수 + 보험가입금액 x 10/1000 [REG-R20], the 해약공제계수 being the 보험기간 capped at 20 years for a 보장성보험 — so on a 종신 contract it is one year’s net premium plus 1% of the sum assured. The 연납순보험료 is taken as 80% of the gross [std], the chassis’s ratio, so that the cap can be reproduced from published quantities rather than from this model’s own pricing basis.

At the anchor that is ₩2,944,704 + ₩1,000,000 = ₩3,944,704. Cross-check: the FSC’s 보장성보험 rule of thumb of 13 times the monthly premium gives ₩3,987,620, which agrees within 1.1% [REG-R29]. The 보험가입금액 that enters the formula is the pre-acceleration death benefit, by 감독규정 [별표 15] 제3호 read with 제8호 [REG-R21]: a CI contract covers death from any cause, so 일반사망 applies directly and the figure is ₩100,000,000 and not the ₩20,000,000 residual — a clean instance of the acceleration form buying this product a simpler regulatory position than a standalone 진단비 product, which must build a notional 보험가입금액 instead.

surr_chg_period_mths()[source]#

12 n_sc: the 해약공제기간 in months.

The 납입기간 or the 신계약비 부가기간 capped at 7 years [REG-R19 제7-66조제1항제2호], multiplied out. The period is a contractual term quoted in years and did not change when the grid did.

surr_chg_pp(t)[source]#

SC(t): the 해약공제액 (미상각신계약비) outstanding at month-end t.

On the month-end clock, t = 0 at issue where the whole cap is outstanding, so a surrender arising in month t bears SC(t + 1).

The cap running off in a straight line over the 해약공제기간, now in 84 monthly steps rather than seven annual ones on the anchor’s 20년납 contract, so the balance deducted is the balance outstanding in the month the surrender is actually taken. The charge is gone by the month-end d = 84, thirteen years before 납입완료 and, on most lives, before any CI event — which is why the step in cv_pp() at 납입완료 is not a surrender-charge effect and cannot be explained as one. The straight-line run-off is [std]: the amortisation schedule lives in the unpublished 산출방법서.

cv_std_pp(t)[source]#

W(t): the 표준형 twin’s 해약환급금 at anniversary t, floored at zero.

max(0, V(t) - SC(t)). The 미경과보험료 that 감독규정 제7-66조제5항 adds on termination is not modelled [std]: premiums are paid monthly in advance on the month-end grid, so at most one instalment is ever unexpired and the monthly step is the finest the composite’s own premium mode makes available.

cv_mult(t)[source]#

The multiplier on W(t) at month-end t: k inside the 납입기간, 1 from 납입완료.

A step, not a ramp, at the 계약해당일 d = 12m. A surrender occurring in the last paying month — t = 12m - 1 — is paid at the end of it, that is at d = 12m, on the full value [std ordering]; the suppressed value applies to the month-ends 1 to 12m - 1. The monthly grid is what makes the step checkable as a step: the two month-ends either side of it are one month apart, so a doubling between them is visibly a single-row event and not an artefact of comparing two balances a year apart. Both quantities exist at every duration and the model publishes both, cv_pp() and cv_pp_ci().

cv_pp(t)[source]#

CV(t): the 해약환급금 payable on a pre-CI surrender at anniversary t.

cv_mult(t) W(t). On the 무해지 form (k = 0) this is nil throughout the 납입기간, and the FSS’s finding that such a contract cannot support a policy loan at all during the payment period [REG-R28] [REG-R25 제33조] follows arithmetically — which is one reason the composite’s representative form is 저해지 rather than 무해지.

cv_pp_ci(t)[source]#

CV’(t): the 해약환급금 payable on a post-CI surrender at anniversary t.

W(t), the full 표준형 value, at every duration, before and after 납입완료 [S2] [S4]. This is the CI-specific delta on the chassis and it is contractual: [S2] conditions the suppression on 「제7조 … 제2호의 CI/LTC보험금 지급사유가 발생하지 않은 경우」 and [S4] on 「「선지급 진단보험금」 지급사유 발생 전 납입기간 동안」.

Three consequences follow and each is a modelling requirement. The surrender strain on the post-CI cohort is materially larger than on the pre-CI cohort at the same duration, so a projection running one surrender-value scale over one aggregate policy count understates outgo. The policy loan available jumps at the same date. And the premium stops at the same date, so from t_CI the contract pays nothing, holds a full-value surrender right and owes only the residual — which is what makes the post-CI state a genuinely different liability rather than a scaled-down version of the pre-CI one.

There is an accounting asymmetry worth naming: the 해약환급금준비금 appropriation test measures the IFRS 17 잔여보장요소 against the surrender value computed under 제7-66조 제1항, on the unsuppressed basis, even for the 제4항 products that may contractually pay less [REG-R11]. So this carve-out doubles the contractual value from one day to the next and changes the reserve it is measured against not at all.

ci_cohort_ids(t)[source]#

The post-CI cohort labels that can carry policies at the start of month t.

[-1 .. -min(t, 12)] + [1 .. t]. A cohort is labelled by the month-end at which its acceleration was paid, so a life accelerating in month u is paid at u + 1 and carries the label u + 1. The negative labels are the first-year 감액 cohorts: a reduced claim paid at the month-end d carries the label -d, which is free precisely because nothing can be accelerated at month-end 0 and no full claim ever carries a negative label.

The monthly grid turns one reduced cohort into twelve. On an annual grid the whole of the first policy year’s reduced claims were paid at one anniversary and carried one residual; here they are paid at twelve month-ends, each off its own 기본보험금, and the first two are empty because no 중대한 암 is covered before the 보장개시일. Entrants join at the start of the month after they accelerate, so no label > t can be populated at t.

accel_benefit_pp(s)[source]#

a B(s): the 선지급 CI/LTC보험금 paid to cohort s, per policy.

a B(s) for a full claim paid at the month-end s, and a f B(-s) for a first-year reduced claim, whose label is the negative of the month-end it was paid at; f = 0.5, so 40% of the 기본보험금 instead of 80% on the composite, 25% instead of 50% on the 50% form [S1 별표1] [S2 별표1]. Paid at the end of the month of the event, once only across the whole trigger set, and not netted against any policy loan: the contract continues and the loan stays outstanding against the residual.

resid_nominal_pp(s)[source]#

r B(s): the nominal residual death benefit cohort s carries, per policy.

The exact complement of what was paid — (1 - a) B(s), and (1 - a f) B(-s) for a first-year reduced cohort, so 60% where 40% was accelerated [S1] [S2]. It is fixed at the acceleration month and does not move afterwards; what moves is the floor beneath it, resid_db_pp(). The monthly grid is what makes 「지급사유 발생 당시의 기본보험금」 a month rather than a policy year.

resid_db_pp(t, s)[source]#

The death benefit payable at month-end t to a policy in cohort s.

Both indices are on the month-end clock, so a post-CI death in month t is paid resid_db_pp(t + 1, s).

max(r B(s), c V(t)) — 「CI/LTC보험금 지급사유 발생당시의 기본보험금의 20%와 CI/LTC보험금 지급사유 발생 후 계약자적립금의 105% 중 큰 금액」 [S1 별표1 주8]. The residual is not a constant, and on the 80% form the floor binds early and stays bound: at the anchor cell r B is ₩20,000,000 and the account passes ₩19,050,000 well inside the 납입기간, so for most of the contract’s life the residual death benefit is the account value and not the stated complement. A model that hard-codes 20% of the sum assured understates the post-CI liability by a growing margin, and that asymmetry is one of the three reasons the composite takes the 80% fraction.

resid_nom_min_pp(t)[source]#

The smallest nominal residual carried by any cohort live at the start of month t.

A running minimum over the cohorts formed so far, and one of the two bounds that let resid_db_total_pp() close in one line in the months where the 105% account floor is either below every cohort’s nominal or above all of them. Infinite — represented as the largest nominal plus one won — while no cohort exists.

resid_nom_max_pp(t)[source]#

The largest nominal residual carried by any cohort live at the start of month t.

The companion running maximum to resid_nom_min_pp().

resid_nom_total_pp(t)[source]#

Sum over the post-CI cohorts of count times nominal residual, at month t.

sum(l1(t, s) r B(s)), carried as its own O(T) recursion rather than rebuilt from the cohort table every month: every post-CI cohort carries the same two decrements, so the aggregate rolls forward exactly as a single cohort would, and the month’s entrants are added at their own nominal.

This is the conversion’s one piece of new machinery and it is there for a reason. The cohort dimension is the acceleration month, so the (month, cohort) table is twelve times longer and a hundred and forty-four times larger than the annual grid’s; summing it row by row in every month is quadratic work for an answer that is almost always available in closed form. See resid_db_total_pp().

resid_db_total_pp(t)[source]#

Sum over the post-CI cohorts of count times payable residual, at month t.

sum(l1(t, s) max(r B(s), c V(t + 1))) — the amounts payable at the month-end that closes month t, which is where a post-CI death in it is paid. It is what claims() weights "DEATH_CI" by and what resid_db_avg_pp() averages.

Three cases, and the first two are exact one-liners:

the floor is below every cohort’s nominal — then the payable residual is the nominal for all of them and the answer is resid_nom_total_pp();
the floor is at or above every nominal — then it is the floor for all of them and the answer is the floor times the count;
otherwise the cohorts straddle the floor and the sum is taken cohort by cohort.

On every shipped model point the third case covers a window of a year or two — the months in which 1.05 V crosses the narrow band the nominals occupy — so the cohort loop runs where it is needed and nowhere else, and the result is the same number a row-by-row sum would give in every month.

resid_db_avg_pp(t)[source]#

The in-force-weighted mean residual death benefit over the cohorts, in month t.

The weights are the post-CI counts at the start of month t and the amounts are the benefits payable at its end, the month-end t + 1, which is the pairing claims() uses for "DEATH_CI".

A reporting quantity only; no cash flow uses it. It is published because the spread between it and r SA is the clearest single reading of how far the 105% floor has taken over the residual.

loan_avail_pp(t)[source]#

The 보험계약대출 available at month-end t to a pre-CI policy.

80% of the payable 해약환급금 [REG-R25 제33조], which during the 납입기간 is the suppressed value. The chassis argues the 80% limit against published Korean ranges of 「해약환급금의 50% ~ 85%」 and 「50 ~ 80%이내」 and this product inherits it.

loan_avail_ci_pp(t)[source]#

The 보험계약대출 available at month-end t to a post-CI policy.

The same 80% of the payable value, which after a CI event is the full 표준형 value — so on the composite’s k = 0.50 form the available loan doubles the moment a CI/LTC 지급사유 arises, at the same duration and with no other change to the contract. Nothing in the retrieved documents restricts the loan after a CI payment, so the post-acceleration contract carries a full-value loan facility against a sum assured that is now a fifth of its original size; whether any carrier restricts it further is [unverified]. Published as its own cells so that the doubling can be read directly rather than inferred.

pol_loan_draw(t)[source]#

Delta(t): the 보험계약대출 drawn at month-end t, per policy; nil in the base run.

pol_loan_year is a contractual duration in policy years — duration 12 on model point 7 — and did not change when the grid did: the draw falls at the 계약해당일 d = 12 * pol_loan_year(), which is the same date it always was, now located to the month.

loan_pp(t)[source]#

L(t): the 보험계약대출 balance at time t, the opening balance of month t.

L(0) = 0 and L(t) = (L(t - 1) + Delta(t))(1 + j_L) on the monthly equivalent of i_L = 예정이율 + 1.5% = 4.00%, the chassis’s rate, so twelve months compound back to exactly the annual figure the 약관 quotes; Delta is pol_loan_draw() on the month-end clock, so a draw is booked with one month’s interest in the month it is taken [std] — this model’s own arithmetic, and identically immaterial in the base run, where nothing is drawn. It is the balance the benefits of month t are netted down by. One balance per policy, carried unchanged across the CI transition — a policy that borrowed before accelerating still owes it afterwards — and deducted from every terminal payment, floored at zero. The 보험계약대출 is a modelled state and not a decrement: no policy leaves because of it here, and a loan that outgrows the benefit simply reduces the payment to nil.

pols_if_pre(t)[source]#

l0(t): policies in force and pre-CI at the start of month t.

Decremented in the month by the CI transition first, then death among those who did not accelerate, then surrender among those who neither accelerated nor died, so l0(t + 1) = l0(t)(1 - q_ci^m)(1 - q^m)(1 - w^m), with l0(0) = pols_if_init().

pols_waived(t)[source]#

Policies in force, pre-CI and on the 장해 50%+ premium waiver at the start of t.

A subset of pols_if_pre(), not a separate state: a waived policy keeps its full death cover, stays exposed to the CI decrement and continues to accrue surrender value on the full premium scale. What it stops doing is paying, so it is subtracted from pols_if_pay() and from the renewal commission that follows the cash. The waiver on the CI limb is not counted here — it is implicit in the post-CI cohort, which pays nothing at all. Nil in the first month, t = 0: nobody has yet been on the waiver.

pols_if_pay(t)[source]#

lp(t): policies in force, pre-CI and actually paying a premium in month t.

l0(t) less the waived subset, and nil once no premium is due. The post-CI cohort never appears here: any CI/LTC 지급사유 waives all future 기본보험료 [S1 별표1 주4], so the residual death benefit is funded entirely out of the reserve standing at the acceleration date — which [S4] states in terms, computing the post-waiver reserve on the post-acceleration basis 「「선지급 진단보험금」 발생 이후 기준의 책임준비금을 계산」.

pols_ci(t)[source]#

C(t): CI/LTC accelerations in month t, taken from the pre-CI cohort.

l0(t) q_ci^m(t). This is a state transition and not an exit: the contract continues, which 감독규정 제7-60조제8호 requires — a contract must not be extinguished while the risk it covers remains effective [REG-R16] — so these policies reappear in pols_if_ci() at the start of the next month and stay in pols_if() throughout.

pols_ci_in(t, s)[source]#

C(t, s): accelerations in month t entering post-CI cohort s.

Cohort t + 1 — the month-end at which the month’s claims are paid — takes the full-benefit claims of month t; cohort -(t + 1) takes the reduced ones, and is empty outside the twelve months of the first policy year.

ci_cohort_entrants(s)[source]#

The policies that entered post-CI cohort s, at the month-end abs(s) it is named for.

A cohort has exactly one entry month by construction — it is labelled by the month-end its acceleration was paid at — which is what lets pols_if_ci_at() be a closed form rather than a recursion in t.

ci_surv(t)[source]#

The post-CI survivorship from issue to the start of month t, ignoring entry.

prod (1 - q'^m(u))(1 - w'^m(u)) over u < t, with ci_surv(0) = 1. Every post-CI cohort carries the same two decrements, so a cohort’s in-force at t is its entry count times the ratio of this factor at t to its value at the entry month — which is pols_if_ci_at(), in closed form and without a recursion per cohort.

pols_if_ci_at(t, s)[source]#

l1(t, s): policies in force and post-CI at the start of month t, from cohort s.

Entrants join at the start of the month after they accelerate, and are then decremented by post-CI mortality and post-CI surrender. Kept by cohort because the residual is a cohort property: see resid_nominal_pp(). Nil at t = 0, and defined one step past the frame at t = proj_len(), the terminal month-end, where the roll-forward checks read it.

Written as entrants(s) x ci_surv(t) / ci_surv(abs(s)) rather than as a recursion in t. The two are the same number; the closed form is what keeps a cohort dimension twelve times longer than the annual grid’s from turning every read of it into a chain of monthly steps.

pols_if_ci(t)[source]#

l1(t): policies in force and post-CI at the start of month t, all cohorts.

Carried as its own recursion — the month’s entrants plus last month’s survivors — and not as a sum over the cohort table. Every post-CI cohort runs the same two decrements, so the aggregate rolls forward exactly as the sum of the cohorts does, and the identity is what check_ci_state_roll_fwd() asserts.

pols_if(t)[source]#

l(t): the total number of policies in force at the start of policy year t.

Pre-CI plus post-CI. A CI claimant’s contract is still in force — that is the whole point of an acceleration — so both states are counted here, and this is the weight on every maintenance-expense figure of the same result_cf() row. It is pols_if_init() in the first month, t = 0, and 0 at proj_len(), because the table terminates and every remaining life dies in the final policy year.

pols_if_at(t, timing)[source]#

The number of policies in force at a point inside month t.

"BEF_DECR": l(t), the start of the month, before anything happens; the same number as pols_if().
"BEF_LAPSE": after the CI transition and after deaths, before surrenders — the processing order is CI, then death, then lapse [std order], so this is the population surrenders are taken from.
"AFT_DECR": l(t + 1), the end-of-month state, and zero at proj_len() - 1 because the table’s terminal rate is 1 and nobody survives the final policy year.

pols_death(t)[source]#

D(t): expected deaths of pre-CI policies in month t, at the end of it.

Taken from the survivors of the CI transition. These policies never received an acceleration, so they are paid the whole 기본보험금 [S1].

pols_death_ci(t)[source]#

D’(t): expected deaths of post-CI policies in month t, at the end of it.

On mort_rate_ci_mth(), which carries the excess mortality a 중대한 질병 event implies. Each cohort is paid its own residual, so the aggregate count here is a reporting figure and the benefit is weighted by resid_db_total_pp() in claims().

pols_lapse(t)[source]#

S(t): expected surrenders of pre-CI policies at the end of month t.

Taken from the survivors of the CI transition and of mortality — CI, then death, then lapse [std order] — and paid cv_pp() net of any loan, which inside the 납입기간 is the suppressed value.

pols_lapse_ci(t)[source]#

S’(t): expected surrenders of post-CI policies at the end of month t.

Paid cv_pp_ci(), the full 표준형 value, at every duration. The surrender strain on this cohort is therefore materially larger than on the pre-CI cohort at the same duration, which is the modelling consequence of the carve-out.

premiums(t)[source]#

Premium income at the start of month t, an inflow.

G^m lp(t), carried on the paying cohort alone: the post-CI cohort pays nothing because any CI/LTC 지급사유 waives the premium, and the 장해 50%+ waived subset pays nothing either. Zero from t = prem_period_mths(); nothing else about the contract stops there.

There is no 자동대출납입 behind the 납입최고 in any retrieved Korean 약관 — a conventional Korean contract is 해지 the day after a 14-day demand period ends [REG-R25 제26조] — so Korean lapse is behavioural rather than funded, and a model that imported the Japanese automatic-premium-loan machinery onto this chassis would remove a decrement the contract has.

claims(t, kind=None)[source]#

Benefit outgo in month t, by kind; the total when kind is omitted.

Every payment here falls at the end of month t, which is the month-end t + 1, so every amount is read off the month-end clock one step ahead of the row: B(t + 1), CV(t + 1), W(t + 1), resid_db_pp(t + 1, s). The loan netted off is loan_pp(t), the balance the month opened with.

"CI": the 선지급 CI/LTC보험금, a B(t + 1) on the full-benefit claims — cohort t + 1 — and a f B(t + 1) on the first-year reduced ones, cohort -(t + 1), paid at the end of the month of the event and not netted against any policy loan, because the contract continues and the loan does with it.
"DEATH": the 사망보험금 of a policy with no prior CI payment, B(t + 1) net of any loan, floored at zero.
"DEATH_CI": the residual death benefit, max(r B(s), c V(t + 1)) net of any loan, summed cohort by cohort because each carries its own nominal.
"LAPSE": the 해약환급금 on a pre-CI surrender, CV(t + 1) net of any loan.
"LAPSE_CI": the 해약환급금 on a post-CI surrender, the full W(t + 1) net of any loan — the carve-out, at every duration.

Every one of these is floored at zero: a loan can outgrow the surrender value and, given long enough, the residual, and none of them may produce a negative payment.

claim_expenses(t)[source]#

The claim handling expense on the month’s claim events [std].

₩300,000 per event, uninflated, on CI accelerations and on both kinds of death. A CI claim is charged the same as a death claim, which is a standardization and probably a generous one: the whole dispute record of this product is about adjudicating the 중대한 definitions, and an accelerated claim on a 중대한 뇌졸중 requires a 장해 assessment deferred twelve months after onset [S1 별표3]. No Korean carrier publishes an expense basis of any kind — [S1] names the components as 계약체결비용 and 계약관리비용 and never quantifies them — so every expense level here is a standardization, bounded above by the 표준해약공제액 [REG-R20] and by the 보험료지수 of 130.1% [S3]. Published as its own claim_expenses column and deducted explicitly in net_cf(); it is not inside expenses().

inflation_factor(t)[source]#

The expense inflation factor in month t: (1 + pi)^(t // 12) [std], 1 at t = 0.

1.0% a year, stepping on the 계약해당일 and level across the twelve months of a policy year — an expense basis is quoted per annum and an inflation assumption with it. Over a seventy-year whole-life horizon 1% compounds to 2.0 and 3% to 7.9, so importing a Western inflation assumption here produces a different product rather than a stressed one. There is no published Korean expense basis to anchor either figure.

expenses(t)[source]#

E0 and e(t) in month t: acquisition and maintenance only [std].

₩500,000 per policy at issue, then ₩5,000 per policy per month inflating at 1% a year, both at the start of the month. Maintenance is carried on pols_if(), the total in force, so a post-CI policy costs the same to administer as a pre-CI one; it continues for life and not to 납입완료, which is the structural point of this chassis. There is no separate surrender expense; it is folded into maintenance [std]. The claim handling expense is not here: it is claim_expenses(), deducted separately and published in its own column.

commissions(t)[source]#

Commission outgo in month t [std].

80% of the annual premium in month 0, then 3% of premium income in the months of policy years 2 to m — t = 12 … 12m - 1, every paying month but the twelve of the first policy year. The initial commission is computed on the annual premium because that is the unit a Korean commission scale is written in: the 1,200% rule of the 2019 사업비 reform caps first-year 모집수수료 at twelve times the monthly premium, which is one annual premium [REG-R29], and the 80% here sits under it and just under the 표준해약공제액 of ₩3,944,704, the statutory bound on what a surrender may be made to repay. Renewal commission follows the premium actually collected in cash, so neither the waived subset nor the post-CI cohort produces any, and none is paid after 납입완료.

net_cf(t)[source]#

CF(t): the net cash flow of month t, income positive.

Premiums less the five kinds of benefit, claim expense, acquisition and maintenance expense and commission. The notes’ own sign, which is also the library-wide convention, so there is no outgo-positive liability_cf companion to publish.

The shape to expect is a deep new business strain in the first month t = 0, where the whole acquisition expense and the whole first-year commission fall against one instalment of premium, a long positive stretch while the premium runs against a CI decrement that is still small, a steepening drain as the incidence curve turns over from the fifties, a negative step at 납입완료 where the premium stops and the suppression lifts, and then a run-off in which the whole of the outgo is claims and maintenance against no income at all. The acceleration front-loads that outgo: on the anchor cell the CI benefit is paid a decade or more before the death benefit it accelerates.

check_pols_roll_fwd_resid(t)[source]#

The total in-force roll-forward residual in month t; zero everywhere.

l(t) - l(t + 1) less deaths and surrenders in both states. The CI acceleration is deliberately absent from this identity: it is a transition and not an exit, and a model in which it reduced the in-force count would be modelling a standalone 진단비 benefit rather than an acceleration.

check_pols_roll_fwd()[source]#: True when the total in-force roll-forward closes in every projected month.

check_ci_state_roll_fwd_resid(t)[source]#

The two-state transition residual in month t; zero everywhere.

Two identities added: the pre-CI cohort loses exactly its accelerations, deaths and surrenders, and the post-CI cohort gains exactly the accelerations and loses exactly its own deaths and surrenders. This is the check that catches a policy accelerating out of one state and not arriving in the other, which the total roll-forward above cannot see.

check_ci_state_roll_fwd()[source]#: True when both cohorts roll forward and the transition between them balances.

check_decrement_sum_resid(t)[source]#

The cumulative-decrement residual at month t; zero everywhere.

l(0) less every exit up to and including month t less l(t + 1). At t = T - 1 it is the statement that the decrements sum to 1: because the table terminates, every policy leaves by a death or a surrender in one of the two states and there is no residual population and no tail state anywhere in this model.

check_decrement_sum()[source]#: True when every policy issued leaves by a modelled decrement, in every month.

check_pol_val_roll_fwd_resid(t)[source]#

The 계약자적립액 recursion residual over month t; zero everywhere.

(V(t) + P^m 1{t < 12m})(1 + j) less q_ci^m [a SA + A1(t+1)] + (1 - q_ci^m) q^m SA + (1 - q_ci^m)(1 - q^m) V(t + 1) on the pricing decrements — the retrospective form of the same prospective value, rolling the account the month opens with, V(t), into the one it closes with, V(t + 1). It is what catches a mis-set 납입기간, a discount factor applied on the wrong side, a CI decrement left out of the premium annuity but present in the benefit, or an annual rate used where its monthly conversion belongs.

check_pol_val_roll_fwd()[source]#: True when the 계약자적립액 rolls forward on its own basis in every month.

check_accel_complement_resid(t)[source]#

The complement residual for every cohort formed in month t; zero everywhere.

The identity this product exists to demonstrate: what is accelerated and what is left add to exactly the 기본보험금 that was in force when the claim arose, a B + r B = B and a f B + (1 - a f) B = B, so the acceleration is a redistribution of one sum assured across two dates and never adds cover [S1] [S2]. Exactly two cohorts can be formed in a month — the full one t + 1 and the reduced one -(t + 1) — so the check reads those two and no others, and a model point whose first policy year carries reduced claims checks both arithmetics.

check_accel_complement()[source]#: True when the acceleration and its residual sum to the 기본보험금, every cohort.

check_resid_floor_resid(t)[source]#

The residual-floor residual for month t; zero everywhere.

Read at the month-end t + 1, the end of the month, which is where a post-CI death in month t is paid. The post-CI death benefit must be at or above both of its limbs — the nominal complement fixed at the acceleration month and 105% of the account now — so the two shortfalls, each floored above at zero, must vanish. A one-sided max written the wrong way round, or a floor read off the wrong month’s account, shows up here and nowhere else.

It is asserted in two forms, because the cohort dimension is now the acceleration month and a full cohort-by-cohort sweep of every month would be quadratic. In every month the aggregate form is checked — the total payable residual against the total nominal and against the floor times the count, which is the same statement summed — and at every 계약해당일 the sweep is taken cohort by cohort as well, so every cohort ever formed is read against both of its limbs at twelve-month intervals and the first-year reduced cohorts are read at the first of them.

check_resid_floor()[source]#: True when the residual death benefit is the maximum of its two limbs, every month.

check_cv_carve_out_resid(t)[source]#

The carve-out residual at month-end t; zero everywhere.

On the month-end clock, so check_cv_carve_out() sweeps 0 … proj_len() rather than the frame.

min(0, CV'(t) - CV(t)). The consumer-protection design the carve-out exists to produce is that a CI claimant is never worse off on surrender than an unaccelerated policyholder at the same duration [S2] [S4], and this is that statement as an inequality with a signed residual. It is not tautological: it fails the moment the suppression is applied to the post-CI cohort, which is the natural mistake to make when one surrender-value scale is run over one aggregate policy count.

check_cv_carve_out()[source]#: True when the post-CI surrender value is never below the pre-CI one.

check_loan_roll_fwd_resid(t)[source]#

The 보험계약대출 roll-forward residual over month t; zero everywhere.

L(t + 1) - (L(t) + Delta(t + 1))(1 + j_L), the balance the month closes with against the one it opened with and the draw taken at its closing month-end. Identically zero in the base run, where there is no loan at all; non-trivial the moment the module is switched on, which is the point of it.

check_loan_roll_fwd()[source]#: True when the loan balance accumulates at j_L in every month.

check_net_cf_resid(t)[source]#

The published cash-flow statement’s residual in month t; zero everywhere.

net_cf() less the published result_cf() columns of the same row. It closes the loop between the total benefit outgo and the five kinds that make it up, so a sixth kind added to claims() and left out of the statement shows up here rather than silently vanishing from it.

check_net_cf()[source]#: True when the net cash flow equals the sum of its published columns, every month.

result_cf()[source]#

Result table of cash flows, indexed by the 0-based month t.

pols_if is the start-of-month count of policies in force in both states, which is the weight on the maintenance expense of the same row; the decrement-weighted figures are in result_pols(). net_cf carries the notes’ own income-positive sign. expenses is acquisition and maintenance; the claim handling expense is beside it in claim_expenses, as in every model in the sister libraries. The five claims_* columns are published rather than their total, so that the columns sum to net_cf and the acceleration can be read apart from the death benefit it accelerates.

result_pols()[source]#

Result table of policy counts and decrement rates, indexed by the month t.

The two states side by side, so that the migration from pols_if_pre to pols_if_ci — which is the product — can be read directly. The three rate columns are the monthly decrements actually applied; their annual parents are mort_rate, ci_rate and lapse_rate, which hold the figures the sources tabulate.

result_val()[source]#

Result table of the account, the surrender values and the benefit levels, by t.

Indexed by the month t, like result_cf(), and every state column is the value at the month-end that closes that month, t + 1 — the amount a claim or a surrender arising in the row’s own month is actually paid. So row t = 0 carries V(1), the account at the first month-end, and the issue-instant values V(0) = 0 and SC(0) = SC_max are one step off the top of the table, reachable from the cells themselves. accel_benefit_pp and resid_nominal_pp are read at the cohort label t + 1, which is the full-benefit cohort the row’s own accelerations form; loan_pp is the balance the row opens with, as in claims().

cv_pp is the amount payable before a CI event and cv_pp_ci the amount payable after one, so the carve-out and the step at 납입완료 can be read off the same table. resid_db_avg_pp against resid_nominal_pp at any duration shows how far the 105% account floor has taken over the residual.