Technical Notes#

Status: Draft, 2026-08-20 (all cited sources accessed 2026-08-20).

Scope note. These notes turn the standardized composite of product-spec.md (same directory) into a reference liability cash-flow projection model on paper. They describe no single insurer’s product. [S#] and [R#] tags resolve in sources.md, whose numbering is carried verbatim from _research/cancer.md and is frozen; [REG-R#] tags resolve in the cross-product reference library references/regulatory-and-actuarial-references.md, whose R-numbering is separate. std marks a standardization introduced for the reference implementation, always with a rationale and, where one exists, the observed range; unverified marks a claim not confirmed against a retrieved document. Every parameter value here is identical to product-spec.md’s. Eleven assumption inputs appear here that product-spec.md does not carry, because they are modelling constructs rather than contractual terms and each is introduced below as such: the first-diagnosis incidence rate, the 上皮内新生物 incidence increment, the post-diagnosis survival basis, the relapse hazard that drives the repeat cycle, the hospitalisation frequency and mean stay for a diagnosed life, the surgery frequency, the qualifying-treatment-month probability, the outpatient-day frequency, and the 先進医療 frequency and severity.

Deltas against the medical insurance (iryō hoken, 医療保険) chassis. The medical technical notes (医療保険) are the third-sector (dai-san-bun’ya, 第三分野) chassis in model form and are not restated here. Five things change, and every one of them changes the shape of the model rather than a parameter in it:

  1. A three-state model, not a one-state model. medical projects a single in-force population and reads a hospitalisation incidence off it. A cancer model cannot: the diagnosis benefit repeats on a two-year cycle, the inpatient benefit has no day limit, and the treatment benefit pays by the month — so all three run on how long the insured lives after diagnosis. This model therefore carries a never-diagnosed state and a diagnosed state, and needs a survival model as well as an incidence model.

  2. The 90-day waiting period is a hard zero in months t = 0, 1, 2. No cancer benefit of any kind is payable, and the premium is [S1] [S5] [S6] [S7] [S10].

  3. No L1 and no LA. The per-hospitalization and lifetime aggregate (tsūsan, 通算) day ledgers that dominate medical do not exist here, and neither does the benefit-driven termination they create [S1] [S3] R11. What replaces them is a 60-month ledger on the treatment benefit, which is a ledger on months, not days.

  4. Carcinoma in situ (jōhinai shinseibutsu, 上皮内新生物) is a second benefit tier, not a discount — a separate benefit at 50% of the diagnosis lump sum, payable once, on its own cap, not triggering the premium waiver [S6] [S11] [S7] [S10].

  5. The premium waiver is correlated with the insured event, not independent of it. It fires on the same first diagnosis that starts every other benefit [S10] [S11], so the premium stream is carried by the never-diagnosed sub-population alone.

Model scope and conventions#

  • Purpose. Project gross best-estimate liability cash flows for a single-policy model point of cancer insurance (gan hoken, がん保険): office premiums, cancer diagnosis lump sum (gan shindan ichijikin, がん診断一時金), the 上皮内新生物 diagnosis benefit, cancer hospitalization benefit (gan nyūin kyūfukin, がん入院給付金), cancer surgery benefit (gan shujutsu kyūfukin, がん手術給付金), monthly cancer treatment benefit (gan chiryō kyūfukin, がん治療給付金), cancer outpatient benefit (gan tsūin kyūfukin, がん通院給付金), advanced-medicine benefit (senshin iryō kyūfukin, 先進医療給付金), maintenance and claim expenses, and commission. The intended sense is the current estimate (genzai suikei, 現在推計) the economic-value solvency regime requires: probability-weighted future cash flows on assumptions re-set at a stated reporting date (kijunbi, 基準日) rather than locked in at issue REG-R15. It is also the shape the 1号収支分析 takes — a forward income-and-outgo projection over at least ten future years, by 区分経理 segment REG-R22.

  • Out of scope, cited not reproduced. Discounting, MOCE, required capital and every reserving basis — standard policy reserve (hyōjun sekinin-junbikin, 標準責任準備金), contingency reserve (kiken junbikin, 危険準備金), the ESR balance sheet and IFRS 17 all consume these cash flows and are pointed at in Valuation and reserve pointers.

  • Projection frequency. Monthly grid. Three of the product’s mechanics are monthly by construction and not by approximation: the 90-day waiting period is three months of the grid, the treatment benefit’s unit of payment is the calendar month [S5] [S10] [S11], and the premium mode is monthly (月払) at every carrier in the composite [S1] [S6] [S11] [S12]. t is the policy month, t = 0, 1, …, proj_len − 1; month t is the interval from t to t + 1 months after the contract date (keiyakubi, 契約日).

  • The waiting period lands on a grid boundary. がん責任開始日 is the 91st day counting the date cover attaches (sekinin kaishibi, 責任開始日) as day 1 [S1] [S5] [S6] [S10] [S13]; two carriers instead write three calendar months [S8] [S11]. On a monthly grid these are the same boundary, t = 3 std, and the model does not claim a precision it does not have. A daily implementation must separate them; the two wordings are recorded in product-spec.md footnote 9.

  • Timing conventions std. Office premium received at the start of month t; maintenance expense at the start of month t; every benefit and the claim-handling expense at the end of month t; decrements at the end of month t, mortality then lapse. Acquisition expense and initial commission at t = 0.

  • Episode convention std. A diagnosis arising in month t pays its lump sum in month t, and the diagnosed life enters the diagnosed state at the end of month t — so the inpatient, surgery, treatment and outpatient benefits that follow the diagnosis begin at t + 1. Rationale: those four benefits are modelled as continuing hazards on the diagnosed state, not as a resolved episode, which is exactly what makes them depend on post-diagnosis survival. The one-month lag is a timing effect on an undiscounted projection; the alternative — recognising a treatment episode in the diagnosis month — is named in the pitfalls list.

  • Age basis. Attained age at the 契約日 with the fraction discarded (man-nenrei, 満年齢), incremented at each 年単位の契約応当日; 契約年齢 is age last birthday at the 契約日 [S8]. Attained age in month t is age(t) = x + floor(t / 12), x the 契約年齢. 第三分野標準生命表2018 is constructed for use on a nearest-birthday age (hoken-nenrei hōshiki, 保険年齢方式) basis R2 REG-R20, so reading it at 満年齢 understates the valuation age by about half a year; the base run accepts the offset and marks it std, with reading at age(t) + 0.5 as a switch. The incidence basis is published by five-year age band R5, so it is read at the band containing age(t) and steps, not glides.

  • Currency. JPY throughout. There is no minor unit in the contract, but expected values are fractional and are displayed to ¥0.01.

  • Model points. One policy at a time, projected on an expected (probability-weighted) basis. Projection is parameterized by point_id; no aggregation logic is specified here.

  • Termination. Whole-of-life cover: the projection runs to the terminal age of 第三分野標準生命表2018, 116 for males and 118 for females REG-R18 REG-R20, so proj_len = 12 × (terminal_age − x + 1) — 924 months for the anchor cell. There is no maturity benefit and no 満期保険金. There is no benefit-driven termination: payment of the diagnosis lump sum neither terminates nor exhausts the contract [S1], and with no day limits the inpatient benefit cannot exhaust it either [S1] [S3] R11. The decrements are death and lapse, and nothing else.

  • Contract boundary. On the whole-of-life (終身) chassis the premium is level and non-participating (mu-haitō, 無配当) with no insurer repricing right [S5] [S6] [S11], so all future premiums and benefits are inside the boundary and the horizon is the whole of life. On the ten-year renewable term (10年更新 定期) model-point flag the renewal reprices, which would ordinarily close the boundary at each renewal; jplib projects that flag to final expiry and records the tension rather than resolving it, exactly as the medical chassis does.

  • Rounding. Intermediates at full double precision. Displayed cash flows to ¥0.01, pols_if and the state split to six decimals, the diagnosed state to eight decimals, and the treatment-month ledger to four decimals of a month std. Monthly rows rounded for display do not re-add to the displayed annual totals; the totals are sums of unrounded values.

Model point attributes#

Attribute

Type

Anchor cell (point_id = 1)

policy_id

str

—

chassis

enum {shushin, teiki}

shushin (終身)

issue_age (x)

int, 満年齢, 20–75

40

sex

enum {M, F}

M

base_amount (A)

基本給付金額, JPY, menu {5,000, 10,000}

10,000

diag_benefit (DB)

JPY, = 100 × A

1,000,000

cycle_months (C)

int, repeat cycle

24

insitu_pct

fraction of DB for 上皮内新生物 ∈ {1.00, 0.50, 0.10}

0.50

daily_amount (D)

がん入院給付金日額, JPY/day, = A

10,000

surg_mult (m_s)

multiple of A per cancer surgery

20

treat_benefit (B_tr)

JPY per qualifying month, = 10 × A

100,000

treat_cap (K)

int months, lifetime cap on the monthly benefit

60

outp_daily

がん通院給付金日額, JPY/day, = A

10,000

wait_months (W)

int months, 90-day waiting period on the grid

3

prem_period

enum {whole_life, to_65}

whole_life (終身払)

premium (P)

JPY per month, office premium, model-point input

3,000 std

prem_mode

enum {monthly, semiannual, annual}

monthly

waiver_trigger

enum {cancer_diag, disability, none}

cancer_diag

adv_rider

bool — がん先進医療特約 (tokuyaku, rider)

true

disch_rider

bool — がん退院一時金

false

repeat_conditioned

bool — second and later payments require treatment

false

issue_date

date

—

premium is an input, not a computed quantity, and on this product that is a stronger statement than on any other in the library. No carrier publishes a rate table for a cancer main contract; the statement of the method of calculating premiums and reserves (sanshutsu hōhō-sho, 算出方法書) is a 基礎書類 filed with the 金融庁 and is not published REG-R2; and for third-sector business there is additionally no standard incidence table and no reference pure premium to fall back on R3. The single retrieved price point is a ten-year term at twice the composite’s benefit amounts on a 2013 calculation basis [S5]. The anchor’s ¥3,000 is a round modelling figure in that neighbourhood and no result in this library depends on its being a market rate.

State variables#

Variable

Description

Updated

pols_healthy(t)

In force at the start of month t and never diagnosed with an 悪性新生物; pols_healthy(0) = 1

monthly recursion

pols_locked(t)

In force, diagnosed, within C months of the last payment trigger

monthly recursion

pols_open(t)

In force, diagnosed, cycle expired, eligible for a repeat payment

monthly recursion

pols_cancer(t)

pols_locked(t) + pols_open(t) — the diagnosed in-force population

derived

pols_if(t)

pols_healthy(t) + pols_cancer(t) — total in force at the start of t

derived

insitu_avail(t)

Probability, per never-invasively-diagnosed policy, that the once-only 上皮内新生物 benefit is still unused; insitu_avail(0) = 1

monthly

treat_months(t)

Qualifying treatment months already paid, per diagnosed life, against the cap K

monthly

adv_paid(t)

先進医療 技術料 reimbursed, per diagnosed life, against the ¥20,000,000 cap

monthly

age(t)

Attained 満年齢 = x + floor(t / 12)

annually

mort_rate_mth(t)

Monthly best-estimate mortality for a never-diagnosed life

lookup

mort_rate_canc_mth(t)

Monthly mortality for a diagnosed life = baseline plus excess hazard

derived

lapse_rate_mth(t)

Monthly lapse, applied after mortality, to never-diagnosed lives only

lookup

inc_rate_mth(t)

Monthly first-diagnosis incidence per never-diagnosed policy

lookup

net_cf(t)

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

monthly

Why three states and not two. The two-year cycle is not a cap and not a lockout on a counter: it is a clock keyed to an event, and the event that restarts it is the previous payment trigger [S5]. A life that has just been paid cannot be paid again for C months; after that it can, on a fresh relapse (再発), metastasis (転移) or new primary, without limit [S5] [S7] [S10]. pols_locked and pols_open are exactly that distinction, and the flow between them is a 24-month delay, not a rate. This clock is emphatically not the 180-day one-hospitalization memory of the medical chassis: different length, different trigger, different consequence. A model that reuses one clock for both is wrong.

Three absences are product facts, not gaps. There is no cash-surrender-value state: the composite is 無解約払戻金型 at every duration under 終身払 [S7] [S10] [S11], so cv_pp does not exist and lapse carries no cash flow. There is no 契約者貸付 / 自動振替貸付 (jidō furikae kashitsuke, automatic premium loan) state: with no surrender value there is nothing to lend against [S1] [S7] [S10] [S11], so a missed premium really does lapse the policy. And there is no death benefit in the composite [S1], so mortality is a pure liability-releasing decrement and claims_death does not exist.

Both ledgers are per diagnosed life, unweighted by pols_cancer. treat_months and adv_paid measure what an individual has consumed, not what the block has. Because diagnosed lives enter at different times, each ledger is carried as a cohort average that is diluted by new entrants (the recursion is given below); that is a documented approximation with a stated direction of error, not an accident.

Assumption inputs#

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

Input

Value

Basis

Waiting period

90 days; cover from the 91st day, t = 3 on the grid

[S1] [S5] [S6] [S10] [S13] R11; grid std

Diagnosis inside the window

Contract void, not merely unpayable; premiums refunded where neither party knew

[S1] [S5] [S10]

Reach of the voidness rule

Not applied where no benefit event occurs within 5 years of がん責任開始日

[S1]

がん診断一時金

100 × A = ¥1,000,000

[S2] [S3] [S13]

Repeat cycle

At most once in any 2 years, no lifetime cap

[S5] [S7] [S10]

Clock measured from

The previous payment trigger date

[S5]

Deeming rule

Still an inpatient the day after the cycle expires ⇒ fresh trigger

[S1]

上皮内新生物 diagnosis benefit

50% of DB, payable once, own cap, not after a full-rate payment

[S6] [S11]

上皮内新生物 elsewhere

Paid in full on every other benefit; does not trigger the waiver

[S7] [S10]

がん入院給付金

D × days, no per-hospitalization and no 通算 day limit

[S1] [S3] [S5] [S6] [S10] [S13] R11

がん手術給付金

20 × A = ¥200,000; unlimited count; simultaneous procedures count as one

[S2] [S6]

がん治療給付金

¥100,000 per calendar month in which a qualifying treatment occurred; several in one month pay once; lifetime cap 60 months

[S5] [S10] [S11]

がん通院給付金

A per qualifying attendance day, treatment-linked, no day limit

[S1] [S7]

Outpatient during a paid stay

Not payable

[S7] [S10]

先進医療

技術料 in full, lifetime cap ¥20,000,000, rider terminates on the cap; cash top-up 10% capped ¥500,000 per 療養

[S1] [S7] [S11]

保険料払込免除

On first 悪性新生物 diagnosis on or after がん責任開始日; 上皮内新生物 does not trigger it

[S10] [S11]

Surrender value

None at any duration under 終身払

[S7] [S10] [S11]

Grace, 月払

To the last day of the month following the 払込期月

[S1] [S6] [S8]

失効 / 復活

Lapse from the day after grace; reinstatement within 1 year, waiting period re-runs from the 復活日

[S1] [S6] [S8]

Termination on payment

None — the contract does not end and cannot exhaust

[S1] [S3] R11

(b) Insurer-discretionary current elements#

This class is nearly empty, and its emptiness is the product fact. The composite is 無配当 wherever the dividend basis is stated [S5] [S6] [S11]: there is no policyholder dividend (契約者配当), so the three sources of surplus (san-rigen, 三利源) framing and the surplus-distribution methods of 施行規則 第30条の2 REG-R9 do not attach. There is no premium review on the 終身 chassis, no MVA and no non-guaranteed charge scale. What remains:

Input

Snapshot value

Basis

Incidence basis (kiken hasseiritsu, 危険発生率)

The insurer’s own, unpublished, in the 算出方法書

REG-R2; the regulator supplies a test, not a table R3 R4 REG-R13

Prospective 支払事由 change

The insurer may vary the treatment-benefit trigger prospectively with 主務官庁 approval and two months’ notice if the public fee schedule changes

[S1] [S5]; not modelled [std scope]

定期 flag renewal rates

Recomputed at each ten-year renewal at then-current rates

[S5] [S7]; base run holds the issue rate flat std

給付倍率 election

On one design the diagnosis benefit is 入院給付金日額 × a 倍率 the policyholder picks from an insurer-set range

[S6]; model-point input, not a projected variable

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

Mortality of the never-diagnosed. 第三分野標準生命表2018 is public, free and machine-readable R1 REG-R18 REG-R19 — the sharp contrast with uklib, which had to proxy subscriber-only tables. But it is a valuation table whose margin runs the wrong way for a best estimate on a morbidity product: death releases the liability, so the table sits deliberately below national mortality, its risk-theory adjustment bounded at 70% below and 85% above the unadjusted rate R2 REG-R20. A best-estimate basis scales it up:

mort_rate(age) = mort_be_factor × q_third_sector(age, sex)

with mort_be_factor = 1.25 std — the reciprocal of 0.80, a round value inside the sourced 70–85% band R2 REG-R20 (its arithmetic midpoint is 0.775, whose reciprocal is 1.29), so the factor unwinds the table’s stated margin and nothing more. This is the same adjustment the medical chassis uses, and the two products must not disagree about it. mort_rate_mth(t) = 1 − (1 − mort_rate(age(t)))^(1/12) std. The product is capped at 1, which binds at the terminal age alone, where the table already carries a sourced q = 1.00000.

The IAJ’s site terms prohibit reproduction and transmission without written consent REG-R21, so jplib ships mort_table.csv as a std construction, never as a copy. The construction is one table for the whole library, built on the union of the individual 第三分野標準生命表2018 rates jplib’s products quote and attribute — 22 anchor rows across the two sexes, 男 q(40) = 0.00076 among them, and the terminal rows 男 q(116) = 1.00000 and 女 q(118) = 1.00000 REG-R18 REG-R19 REG-R20 — graduated log-linearly (geometrically) between adjacent anchors:

q(x) = q(a) × ( q(b) / q(a) )^((x − a) / (b − a))     for a ≤ x ≤ b, a and b adjacent anchors

Two properties earn the choice. It reproduces every quoted rate exactly, so nothing sourced is disturbed by the graduation; and it is locally the Gompertz family, which is the family the publisher itself uses at the older ages. Each row’s provenance column says whether it is an anchor quoted under attribution or an interpolation between two of them, and points at REG-R18 and REG-R19 either way. The file shipped in this directory is cut to the ages this model can reach — male 20–116, female 20–118 — which is the composite’s issue-age range through to each sex’s terminal age.

Incidence — and this is the one assumption in jplib that is genuinely sourced. For third-sector business the FSA states flatly that no standard incidence rate and no reference pure premium exist, and that insurers must build the rate for each 支払事由 from public data and their own experience R3. For cancer the public data is excellent. The national cancer registry (zenkoku gan tōroku, 全国がん登録), collected under 「がん登録等の推進に関する法律」, publishes 罹患数 and 罹患率 by five-year age band, site, sex and diagnosis year, freely downloadable R5 REG-R29. Age-specific crude rates per 100,000, both sexes, 2023, all sites C00–C96 R5:

band

15–19

20–24

25–29

30–34

35–39

40–44

45–49

50–54

55–59

rate

16.51

24.38

40.14

75.77

132.21

220.28

340.48

453.38

641.76

band

60–64

65–69

70–74

75–79

80–84

85–89

90–94

95–99

100+

rate

959.00

1,406.59

1,948.71

2,306.96

2,459.27

2,497.39

2,360.63

2,275.13

1,889.77

A unisex basis is materially wrong at every age, because the male and female curves cross: at 35–39 female incidence is 193.89 against male 72.92, and at 70–74 male 2,684.60 against female 1,291.07 R5. The published age-banded rates above are both sexes combined, and the by-sex age-band grid was not extracted band by band, so the sex split is a std construction anchored on those two sourced pairs:

f_male(a) = linear interpolation in a of  male / both-sexes rate,
            from 0.551547 at band midpoint 37.5   (72.92 / 132.21)
            to   1.377629 at band midpoint 72.5   (2,684.60 / 1,948.71)   [R5]

mid(age)         = band(age) + 2.5      the midpoint of the five-year band   [std]
inc_rate(age, M) = inc_both(band(age)) × f_male(mid(age))
inc_rate(age, F) = inc_both(band(age)) × (2 − f_male(mid(age)))     [std]

f_male is read at the band midpoint, not at the attained age std: the band rate it scales is itself a band figure, so scaling it by a factor that glides inside the band would give the annual rate a slope the registry does not publish. Reading at the midpoint keeps the whole annual rate a step function, which is the pitfall below.

f_male is clamped to [0, 2] std, and the clamp is not decoration. Outside that interval one limb of the construction goes negative, and a negative incidence is not a rate: the linear form reaches 2 at age 98.87, so at the 100+ band midpoint of 102.5 it gives a female factor of −0.085699 and a female rate of −162.0 per 100,000 — on a projection that runs to attained age 118 for a female life. The admissible domain of a construction whose two limbs must sum to twice the band rate and must both be non-negative is exactly f_male between 0 and 2, and the clamp binds on the 100+ band alone.

Two properties of the construction are validation targets rather than claims. f_male = 1 at age 56.5, against a sourced crossover somewhere between about 25 and about 55 R5. And the female limb does not reproduce the sourced female rates exactly: it gives 191.5 at 35–39 against 193.89 (−1.2%) and 1,212.8 at 70–74 against 1,291.07 (−6.1%) R5, because inc_both is a population-weighted average rather than the arithmetic mean the 2 − f_male form assumes. The error is small at the anchor age and material in the tail; it disappears the moment the by-sex grid replaces the construction. At the anchor cell, f_male(42.5) = 0.669559 and inc_rate(40, M) = 220.28 × 0.669559 = 147.49 per 100,000 = 0.00147490 per year. inc_rate_mth(t) = inc_rate(age(t), sex) / 12 std (uniform within the band year). Any user should replace the whole construction with the by-sex grid from the same workbook — that is what the provenance column is for, and the attribution string the dataset requires must travel with it R5 REG-R29.

上皮内新生物 incidence. The registry publishes paired rows with and without 上皮内がん: 全部位 C00–C96 at 993,469 against 全部位（上皮内がん含む）C00–C96 D00–D09 at 1,114,642, an increment of 121,173 cases, 12.2% of the invasive count R5. The model takes

insitu_rate(age, sex) = 0.122 × inc_rate(age, sex)          [std age-invariance]

The 12.2% is sourced; its age-invariance is std and is very likely wrong in a knowable direction (in-situ detection is screening-driven and concentrated at the screened ages), but the age-banded breakdown on the in-situ-inclusive basis was not confirmed cell by cell R5.

Post-diagnosis survival — the assumption a cancer model has that a medical model does not. 全国がん登録 publishes five-year relative survival (5年相対生存率) by site, sex and 臨床進行度: for 2018 diagnoses, all sites, 63.17% male and 66.84% female R6 REG-R28. Relative survival already nets out background mortality, so it converts directly into an excess hazard without double-counting:

mu_ex(sex) = −ln(S5(sex)) / 5                                       [std, flat]
mort_rate_canc_mth(t) = 1 − (1 − mort_rate_mth(t)) × exp(−mu_ex / 12)

Male: mu_ex = −ln(0.6317)/5 = 0.0918681 per year. Two honest statements come with it. First, the hazard is held flat for the whole diagnosed lifetime std, which overstates late-duration mortality — real relative-survival curves flatten as the cured fraction emerges — and therefore understates the repeating diagnosis benefit and the unlimited inpatient benefit, which are precisely the long-survivor benefits. A duration-banded excess hazard is a switch, and it needs cohort tracking the base run does not carry. Second, the never-diagnosed keep the population table rate, which already contains cancer deaths, so the aggregate double-counts cancer mortality inside the table’s own rates; at the anchor age the table rate 0.00095 is 1% of the excess hazard and the effect is second-order, but it grows with age and a net_of_cancer baseline is a switch. Neither point can be resolved from a source: R6 is a relative survival table, not a cohort mortality table, and any post-diagnosis survival model built on it is a std construction R6.

The relapse hazard — the largest single std lever in the product. Once a diagnosed life’s cycle has expired it becomes eligible again on a fresh 再発／転移／新生 [S5], and the composite does not condition the payment on being under treatment (repeat_conditioned is a switch, because two of the three sourced two-year designs do condition it [S7] [S10]). No public source gives a relapse rate. The model takes

rel_rate = 0.06 per year   ⇒  rel_rate_mth = 0.005          [std]

with the deeming rule (a continuing hospitalisation at cycle expiry is a fresh trigger [S1]) folded into it. The calibration target is stated so it can be argued with: at the anchor cell’s decrement rates held flat, a diagnosed life survives the 24-month lock with probability (1 − 0.0077050)^24 = 0.830575, then wins the race between relapse and exit with probability 0.005 / (0.005 + 0.0077050) = 0.393544, giving p = 0.326868 per cycle and an expected p / (1 − p) = 0.485593 repeat payments, i.e. 1.485593 diagnosis payments per diagnosed life. Read the two numbers apart: p = 32.7% of diagnosed lives collect at least a second lump sum and p² = 10.7% at least a third, and it is the lives collecting three and more that lift the expected count to 0.4856. A third of diagnosed lives paid twice is the design intent of a repeating benefit with no lifetime cap. There is no observed range.

Hospitalisation of a diagnosed life. The mean stay is sourced: 退院患者平均在院日数 for 悪性新生物 discharges in September 2023 was 14.4 days, against 28.4 days for all conditions, with a mild age gradient (35–64: 10.7; 65+: 15.5; 75+: 17.6) R7 REG-R27. The base run uses the all-ages 14.4 and carries the age gradient as a switch std, because the gradient is published on four broad bands and the incidence on twenty-one narrow ones. The frequency is derived from two sourced counts, and the derivation needs no population figure at all because the population cancels:

admissions per diagnosed person (lifetime)
    = ( 推計入院患者数(悪性新生物) × 365 / 平均在院日数 ) / 罹患数
    = ( 106,100 × 365 / 14.4 ) / 993,469
    = 2.707020                                    [R7] [R5]; stationarity [std]

— 2,689,340 cancer admissions a year against 993,469 new diagnoses a year. At 14.4 days each that is 38.98 inpatient days per diagnosed person over a cancer lifetime, which is the single most useful number in this file for sanity-checking an implementation. Spreading it over the diagnosed state at a constant hazard, and using the mean diagnosed-state duration 1 / mort_rate_canc_mth = 129.79 months = 10.815 years implied by the survival basis above:

hosp_rate = 2.707020 / 10.815 = 0.250293  →  0.25 admissions per diagnosed
            life-year                                              [std]

The rounding is to two decimals and the derivation is the rationale. Note what the constant hazard does and does not claim: it makes the inpatient benefit proportional to survival, which is the product’s actual economics under an unlimited-day design, and it does not front-load admissions onto the diagnosis month, which real cancer treatment does. The front-loaded alternative is a switch and is named in the pitfalls list.

Surgery. surg_per_hosp = 0.35 std payable cancer surgeries per cancer admission, carried over unchanged from the medical chassis so the two products do not disagree about the same statistic; 患者調査 crosses 退院患者数 with 手術の有無 but those e-Stat tables were not downloaded for this product R7 REG-R33. The implied lifetime figure is 0.35 × 2.707 = 0.947 payable surgeries per diagnosed person — about one — which is the sanity check. For 上皮内新生物 the composite pays the surgery benefit in full [S7], and in-situ disease is by definition managed by local excision, so surg_per_insitu = 0.80 std surgeries recognised in the in-situ diagnosis month.

上皮内新生物 generates no continuing exposure std. The composite gives an in-situ diagnosis the reduced lump sum and the surgery benefit and nothing else: no inpatient, no treatment months, no outpatient days, and no state change. The rationale is a data fact rather than a convenience: the sourced 推計患者数 and 平均在院日数 figures are for 悪性新生物 and do not measure in-situ exposure R7, so attaching the invasive frequencies to in-situ lives would credit them with an exposure no retrieved statistic observes. The direction of the error is stated: it understates the in-situ tier.

Qualifying treatment months. treat_prob = 0.10 std — the probability that a diagnosed life has at least one qualifying chemotherapy, hormone-therapy or radiotherapy month in a given month, i.e. 1.2 qualifying months per diagnosed life-year. No public source gives it, and there is no observed range. The only calibration anchor is the cap itself: at 0.10 and the diagnosed-state duration above, a life diagnosed at the anchor age accumulates an expected 0.10 × 129.79 = 12.98 qualifying months against the 60-month cap two carriers write [S5] [S11], so the cap binds for a long-course minority — which is what a 60-month cap is for. The benefit is an indicator per month, not a count and not a duration: a prescription covering two months pays one month and two triggers in one month pay once [S10] [S11].

Outpatient days. outp_days = 1.10 std qualifying attendance days per diagnosed life-year, derived on the same population-cancelling trick as the admissions rate: 推計外来患者数 for 悪性新生物 was 186,400 on the survey day R7; at 250 std outpatient operating days a year that is 46,600,000 cancer outpatient visits, or 46,600,000 / 993,469 = 46.91 visits per diagnosed person over a cancer lifetime. The composite’s benefit is treatment-linked — attendance for surgery, radiation, thermal therapy or non-oral chemotherapy [S1] [S7] — not attendance for follow-up, so a 25% std qualifying share gives 11.73 days, and 11.73 / 10.815 = 1.084 per diagnosed life-year, taken as 1.10. Both the 250 and the 25% are unsourced; between them they are a factor-of-four uncertainty on this benefit.

先進医療 std. adv_freq = 0.012 療養 per diagnosed life-year and adv_sev = ¥600,000 per 療養, both std with no observed range. The medical chassis carries the sourced 先進医療 cost anchors (see the medical technical notes (医療保険)); this product’s own source set does not, so neither figure can be tagged here. The severity is set well above the medical chassis’s population-wide figure because a cancer-only trigger selects for particle-beam therapy, which is the expensive end of the 先進医療 list; the direction is defensible and the level is not sourced.

Lapse std. The only published industry-wide persistency figure in Japan is 解約・失効率 5.6% p.a. on 個人保険, measured on opening in-force sum assured REG-R31 — a sum-assured-weighted rate on a book dominated by death cover, which a がん保険 with no sum assured cannot even enter, and no cancer-specific persistency source was retrieved. The table is the medical chassis’s, unchanged, so the two third-sector products share a persistency basis:

Policy year

1

2

3

4

5

6–20

21+

lapse_rate std

9.0%

7.0%

6.0%

5.5%

5.0%

4.5%

3.0%

lapse_rate_mth(t) = 1 − (1 − lapse_rate(year(t)))^(1/12) std. The first ten years average 5.5%, at the sourced 5.6% REG-R31.

Lapse applies to the never-diagnosed only std. This is a product fact, not a refinement. The waiver fires on the first 悪性新生物 diagnosis [S10] [S11], a diagnosed life therefore has no premium to miss, and there is no surrender value to cash in [S7] [S10] [S11] — so there is no mechanism by which a diagnosed policy leaves the book other than death. lapse_rate_canc_mth = 0 in the base run, with a non-zero value as a switch for the disability-trigger and no-waiver designs [S1] [S5] [S6] [S7].

Expenses and commission (all levels std; no Japanese cancer expense or commission scale is public). Carried from the medical chassis, scaled to this product’s premium.

Input

Value

Basis

Acquisition expense

¥20,000 per policy at t = 0

std

Initial commission

1.5 × annualized premium at t = 0 (¥54,000 on the anchor)

std

Renewal commission

3.0% of premiums from policy year 2

std

Maintenance expense

¥250 per policy per month, inflating 1.0% p.a. at each anniversary

std

Claim expense, diagnosis

¥5,000 per diagnosis trigger (invasive or in-situ)

std

Claim expense, hospitalisation

¥3,000 per cancer admission

std

Expense inflation

1.0% p.a. flat

std

Cash flow components and recursions#

Notation#

Symbol

Meaning

t

policy month, t = 0, 1, …, proj_len − 1

x, age(t)

契約年齢 (満年齢); attained age x + floor(t/12)

y(t)

policy year, floor(t/12) + 1

W

waiting period in months (3); cover(t) = 1{t ≥ W}

A, DB

基本給付金額 (10,000); diagnosis lump sum 100 × A

D, m_s

がん入院給付金日額 (= A); surgery multiple of A (20)

B_tr, K

monthly treatment benefit (10 × A); lifetime cap in months (60)

C

repeat cycle in months (24)

u

上皮内新生物 grading of the diagnosis benefit (0.50)

i(t)

monthly first-diagnosis incidence, inc_rate(age(t), sex) / 12

iz(t)

monthly 上皮内新生物 incidence, 0.122 × i(t)

r

monthly relapse hazard once the cycle is open (0.005)

q(t), q_c(t)

monthly mortality, never-diagnosed / diagnosed

w(t), w_c(t)

monthly lapse, never-diagnosed / diagnosed (w_c = 0)

mu_ex

annual excess hazard from 5年相対生存率

h

monthly cancer admissions per diagnosed life (0.25 / 12)

L

mean cancer stay in days (14.4)

s_h, s_z

surgeries per admission (0.35); per in-situ diagnosis (0.80)

p_tr

probability of a qualifying treatment month (0.10)

o

monthly qualifying outpatient days per diagnosed life (1.10 / 12)

f_a, S_a, LV

先進医療 monthly frequency, mean 技術料, lifetime cap (¥20,000,000)

M(t), V(t)

treatment-month ledger; 先進医療 ledger, both per diagnosed life

Z(t)

insitu_avail(t)

P, e(t)

monthly office premium; monthly maintenance expense

ec_d, ec_h

claim expense per diagnosis trigger; per admission

Dimensional check. i, iz, r, q, q_c, w, h, p_tr and f_a are dimensionless probabilities per month; mu_ex is a hazard per year and appears only as exp(−mu_ex/12). L and o are days, M and K are months, s_h is surgeries per admission and s_z surgeries per in-situ diagnosis. D is JPY/day, so D × L is JPY per admission and D × L × h × pols_cancer(t) is JPY per policy-month. B_tr is JPY per month, so B_tr × p_tr is JPY per policy-month directly — no day count enters the treatment benefit at all, and inserting one is the commonest way to break this product. DB, S_a, V, LV, P, e, ec_d and ec_h are JPY. Every net_cf term is JPY per month. The error this check catches: medical’s benefit is 日額 × days and this product’s central benefit is 月額 × months; the two have different dimensions and cannot share a formula.

The waiting period#

cover(t) = 1 if t ≥ W = 3, else 0

and cover(t) multiplies every cancer benefit, the incidence transition and the in-situ transition. In months 0, 1 and 2 the model pays nothing, transitions nobody, and collects the premium [S1] [S5] [S6] [S7] [S10]. It is a hard zero, not a reduced rate.

The invalidity rule is not modelled in the base run and the omission is quantified rather than waved at. A diagnosis inside the window makes the contract void [S1] [S5] [S10] — a de-recognition, not a decrement: the policy was never in force, so it releases the premium already collected as well as the future benefit, and it belongs in a validity adjustment at outset, not in the lapse column. At the anchor cell the probability is 1 − (1 − 0.000122909)^3 = 0.000368681, 0.037% of policies against at most three months of premium, and the composite additionally does not apply the treatment at all where no benefit event occurs within five years of the がん責任開始日 [S1]. The void_adjust switch implements the de-recognition; the base run leaves it off and says so.

On 復活 the waiting period re-runs from the 復活日 [S1] [S6], so a reinstated policy is a different model point with W measured from a new date — which is why reinstatement is modelled as a new model point rather than as a negative lapse.

The diagnosis benefit and the two-year cycle#

diag_first(t) = pols_healthy(t) × i(t) × cover(t)
diag_rep(t)   = pols_open(t)    × r    × cover(t)
trig(t)       = diag_first(t) + diag_rep(t)
claims_diag(t) = DB × trig(t)

with no limit on the number of payments [S5] [S7] [S10] and no termination on payment [S1]. The cycle is a delay, and the delay is implemented on the trigger history rather than as a rate:

unlock(t) = trig(t − C) × Π_{v = t−C}^{t−1} (1 − q_c(v)) (1 − w_c(v)),   t ≥ C
          = 0                                                            otherwise

sc(t) = (1 − q_c(t)) × (1 − w_c(t))

pols_locked(t+1) = ( pols_locked(t) + trig(t) )     × sc(t) − unlock(t+1)
pols_open(t+1)   = ( pols_open(t) − diag_rep(t) )   × sc(t) + unlock(t+1)

Read the two lines together: a life triggered in month t — first diagnosis or repeat — enters locked, survives C months of diagnosed decrements, and arrives in open in month t + C. With repeat_conditioned = true the second and later payments additionally require the insured to be in treatment [S7] or hospitalised [S10]; the switch multiplies r by the conditional probability of being in treatment, which on the std basis is p_tr — and the two designs therefore differ by an order of magnitude, not by a rounding.

The 上皮内新生物 tier#

insitu_ev(t)    = pols_healthy(t) × Z(t) × iz(t) × cover(t)
claims_insitu(t) = u × DB × insitu_ev(t)
Z(t+1)           = Z(t) × ( 1 − iz(t) × cover(t) )

The benefit is payable once over the policy term, on its own cap, and is not payable once a full-rate benefit has been paid [S6] [S11] — which is why it attaches to pols_healthy alone and why Z is a separate ledger rather than a flag on the diagnosis benefit. It does not move the life out of pols_healthy, does not start the two-year cycle, and does not trigger the premium waiver [S7] [S10]. It is a second tier of benefit at a second rate, and the three sourced treatments of in-situ — full rate [S1] [S5] [S10] [S13], half rate [S6] [S11], 10% [S7] — are a single model-point parameter insitu_pct.

The care benefits, all on the diagnosed state#

claims_hosp(t)      = D × L × h × pols_cancer(t)
claims_surgery(t)   = m_s × A × ( s_h × h × pols_cancer(t) + s_z × insitu_ev(t) )
paid_months(t)      = min( p_tr, max(0, K − M(t)) )
claims_treat(t)     = B_tr × paid_months(t) × pols_cancer(t)
claims_outpatient(t)= A × o × pols_cancer(t)
pay(t)              = min( S_a, LV − V(t) )
claims_advanced(t)  = f_a × ( pay(t) + min(0.10 × pay(t), 500,000) ) × pols_cancer(t)

At the anchor cell’s parameters each is a fixed yen amount per diagnosed life-month, and the five numbers are worth memorising as an implementation check: ¥3,000.00 inpatient, ¥1,458.33 surgery, ¥10,000.00 treatment, ¥916.67 outpatient and ¥660.00 advanced medicine — ¥16,035.00 per diagnosed life-month in total.

The two ledgers are cohort averages over the diagnosed population, diluted by new entrants:

M(t+1) = ( M(t) + paid_months(t) ) × pols_cancer(t) / ( pols_cancer(t) + diag_first(t) )
V(t+1) = ( V(t) + f_a × pay(t) )   × pols_cancer(t) / ( pols_cancer(t) + diag_first(t) )

with M = V = 0 while pols_cancer = 0. Only diag_first dilutes: a repeat trigger is an already-diagnosed life whose ledgers continue. The direction of the approximation is the same one the medical chassis records for its day ledger — E[min(Σ, K)] ≠ min(E[Σ], K), so a deterministic average understates the cap’s bite. Here the understatement matters more than it does on medical, because the 60-month cap is reached by a real minority (12.98 expected months against 60) rather than never.

Processing order#

For t = 0, 1, …, proj_len − 1:

  1. Start of month. premiums(t) = P × pols_healthy(t) — the never-diagnosed sub-population only, because the waiver fires on the first invasive diagnosis [S10] [S11]; maintenance e(t) × pols_if(t) with e(t) = 250 × 1.01^floor(t/12); renewal commission 0.03 × premiums(t) for t ≥ 12. At t = 0 additionally the acquisition expense ¥20,000 and the initial commission 1.5 × 12P.

  2. Look up the age basis. age(t), hence mort_rate(age(t)) and the five-year incidence band, hence i(t), iz(t), q(t) and q_c(t).

  3. Apply cover(t). Below W every cancer term is zero, so step 4 produces nothing at all and step 5 applies the two decrements to a population that is entirely healthy.

  4. End of month — triggers and claims. diag_first(t), diag_rep(t), insitu_ev(t), then the seven claim lines above and the claim-handling expense ec_d × (trig(t) + insitu_ev(t)) + ec_h × h × pols_cancer(t).

  5. End of month — decrements, mortality then lapse [std order], on the two populations separately, with no benefit-driven termination:

    pols_healthy(t+1) = ( pols_healthy(t) − diag_first(t) ) × (1 − q(t)) × (1 − w(t))
pols_locked(t+1), pols_open(t+1)  per the cycle recursion above

    A life diagnosed in month t leaves pols_healthy before the decrement and takes the diagnosed mortality in its month of diagnosis std. Lapse pays nothing — there is no surrender value [S7] [S10] [S11] — so claims_lapse(t) is identically zero, and that zero is a product fact worth publishing.

  6. Ledger update. Z(t+1), M(t+1), V(t+1) per the recursions above.

Net cash flow#

net_cf(t) = premiums(t)
          − claims_diag(t) − claims_insitu(t) − claims_hosp(t)
          − claims_surgery(t) − claims_treat(t) − claims_outpatient(t)
          − claims_advanced(t)
          − expenses(t) − claim_expenses(t) − commissions(t)

with

expenses(t)       = e(t) × pols_if(t) + 20,000 × 1{t = 0}
claim_expenses(t) = ec_d × ( trig(t) + insitu_ev(t) ) + ec_h × h × pols_cancer(t)
commissions(t)    = 1.5 × 12P × 1{t = 0} + 0.03 × premiums(t) × 1{t ≥ 12}

expenses is acquisition and maintenance only and the claim-handling cost is a line of its own, deducted explicitly here and published as its own claim_expenses column. The split is library-wide, and on this product it earns itself: the first rides on pols_if, which a waiver does not reduce, and the second on the diagnosis and admission counts, which are the diagnosed state.

net_cf is income-positive in the shipped model, per the library convention. Note the asymmetry that defines the product’s cash-flow signature: premiums are weighted by pols_healthy and claims by pols_cancer, and the two are disjoint. Weighting premium by pols_if overstates income by exactly the waived population.

Policyholder behavior modeling#

  • Lapse is real and immediate — for the never-diagnosed. On a product with a surrender value (kaiyaku-henreikin, 解約返戻金) the insurer would advance an unpaid premium under 自動振替貸付, which REG-R14 requires be at the policyholder’s election with prompt notice; the composite has no surrender value, so neither 契約者貸付 nor 自動振替貸付 can operate [S1] [S7] [S10] [S11]. On the one retrieved cancer contract that does carry a value, the APL runs at ≤ 8% p.a. compounded until principal plus interest would exceed the surrender value [S6], and a model that lapses that contract on a missed premium is wrong; that is a switch, not the base.

  • Grace [std scope]. Grace runs to the last day of the month following the 払込期月 [S1] [S6] [S8]; two months at one carrier [S11]. The base run applies lapse at the end of the month in which the premium is missed and does not model the one-month lag, nor the grace-window rule under which a claim is paid net of the arrears and two months’ premium is deducted where the event falls on or after the anniversary inside the window [S1] [S6].

  • Reinstatement (復活) — and on this product it is not a persistency detail. Available within one year at the composite [S1] [S8]; three years at one carrier [S6]; not at all at another [S11]. What makes it structural here is that the 90-day waiting period re-runs from the 復活日 [S1] [S6]: a reinstated cancer policy is a policy with 90 days of no cover in front of it, which is a genuine anti-selection control. It therefore enters the model as a new model point, not as a negative lapse, and the base run treats lapse as absorbing. One carrier additionally refuses reinstatement outright once any cancer benefit has been paid [S1] — a control conditional on the claim history the model is already carrying.

  • Anti-selective lapse std (optional module, off in the base run). Healthy lives lapse first, so the persisting never-diagnosed block is progressively impaired on the incidence basis:

    inc_eff(t) = inc_rate(age(t), sex) × [ 1 + lam × max(0, w_cum(t) − w_ref) ]

    with w_cum(t) the cumulative lapse proportion among the never-diagnosed, w_ref = 0.20 and lam = 0.30 std. Base run lam = 0. No Japanese evidence was retrieved. On this product the effect is amplified by the waiver: the healthiest lives are also the only ones still paying.

  • No dynamic lapse from surrender value or interest. With no cash value, no assumed interest rate (yotei riritsu, 予定利率) disclosure on this chassis and no MVA, there is no economic surrender trigger. The 低解約返戻金型 cliff that drives the whole_life surrender spike has no analogue here.

  • Elections are not behaviour. base_amount, insitu_pct, treat_cap and the rider set are fixed at issue; benefit reduction (減額) is available on request with fresh underwriting for any increase [S1] [S6] [S12] and is not projected. A model that lets them move over t is modelling a contract term that does not exist.

  • クーリング・オフ. Out of scope: a pre-inception decrement, eight days from dispatch under 保険業法 第309条 REG-R36 and contracted to fifteen at one carrier [S1]. Modelling it would need a new-business funnel this library does not have.

Worked example#

Anchor cell (point_id = 1). Male, 契約年齢 40 (満年齢), 終身 chassis, 終身払, 基本給付金額 A = ¥10,000; がん診断一時金 DB = ¥1,000,000 on a C = 24-month cycle with no lifetime cap; 上皮内新生物 at 50% of DB, once; がん入院給付金日額 D = ¥10,000 with no day limit; がん手術給付金 20 × A = ¥200,000; がん治療給付金 ¥100,000 per qualifying month capped at K = 60 months; がん通院給付金日額 ¥10,000; 先進医療特約 attached; premium waiver on first 悪性新生物 diagnosis; がん退院一時金 off; repeat_conditioned false; void_adjust off; office premium P = ¥3,000 per month; W = 3 months.

Assumption values used, every one of them:

  • Incidence. 罹患率 at 40–44, both sexes, all sites, 2023 = 220.28 per 100,000 R5; std male factor f_male(42.5) = 0.551547 + (1.377629 − 0.551547) × 5 / 35 = 0.669559 from the two sourced pairs R5; so inc_rate(40, M) = 0.00147490 per year and i = 0.000122909 per month.

  • 上皮内新生物. iz = 0.122 × i = 0.0000149949 per month, from the sourced 121,173 / 993,469 = 12.2% increment R5; age-invariance std.

  • Mortality, never-diagnosed. 第三分野標準生命表2018 男 q(40) = 0.00076 R1 REG-R18 — quoted here because a worked example needs it and jplib quotes only the rates it uses REG-R21. It is an anchor of the shipped construction, reproduced exactly, so the worked example reads a sourced rate and not an interpolation. Best estimate mort_rate(40) = 1.25 × 0.00076 = 0.00095 std; q = 1 − (1 − 0.00095)^(1/12) = 0.0000792012.

  • Mortality, diagnosed. 5年相対生存率, male, all sites, 2018 diagnoses = 0.6317 R6 REG-R28; mu_ex = −ln(0.6317)/5 = 0.0918681 p.a. [std flat]; q_c = 1 − (1 − 0.0000792012) × exp(−0.0918681/12) = 0.0077050451.

  • Lapse. Policy year 1, lapse_rate = 9.0% std; w = 1 − (1 − 0.09)^(1/12) = 0.0078284203. w_c = 0 std — a waived life cannot lapse.

  • Relapse. r = 0.06 / 12 = 0.005 per month std. Zero in every row below: the first unlock cannot occur before t = C + W = 27.

  • Cancer care per diagnosed life-month. h = 0.25/12 = 0.0208333 admissions std, L = 14.4 days R7 REG-R27, s_h = 0.35 std, p_tr = 0.10 std, o = 1.10/12 = 0.0916667 days std, f_a = 0.012/12 = 0.001 std at S_a = ¥600,000 std. Hence ¥3,000.00 + ¥1,458.33 + ¥10,000.00 + ¥916.67 + ¥660.00 = ¥16,035.00 of benefit per diagnosed life-month.

  • In-situ surgery. s_z = 0.80 std, so an in-situ diagnosis pays 0.80 × 200,000 = ¥160,000 of surgery benefit per event alongside the ¥500,000 lump sum.

  • Expenses. e(t) = ¥250 (policy year 1) and acquisition ¥20,000 — together the expenses line; ec_d = ¥5,000 and ec_h = ¥3,000 — together the claim_expenses line; initial commission 1.5 × 12 × 3,000 = ¥54,000; renewal commission 3% from t = 12, so zero in every row below std.

Every decrement rate above is either quoted from 第三分野標準生命表2018 R1 REG-R18, from 全国がん登録 R5 R6 REG-R28 REG-R29 or from 患者調査 R7 REG-R27 with its citation, or is marked std as an illustrative value in the shape of such a table. None of them is an insurer’s basis, and none could be: the 算出方法書 is not published REG-R2 and there is no standard third-sector incidence table to substitute for it R3.

In-force and non-claim lines.

t

pols_if

pols_healthy

pols_cancer

premiums

expenses

claim_expenses

commissions

0

1.000000

1.000000

0.00000000

3,000.00

20,250.00

0.0000

54,000.00

1

0.992093

0.992093

0.00000000

2,976.28

248.02

0.0000

0.00

2

0.984249

0.984249

0.00000000

2,952.75

246.06

0.0000

0.00

3

0.976466

0.976466

0.00000000

2,929.40

244.12

0.6733

0.00

4

0.968745

0.968626

0.00011909

2,905.88

242.19

0.6753

0.00

5

0.961085

0.960849

0.00023631

2,882.55

240.27

0.6773

0.00

Claim lines.

t

claims_diag

claims_insitu

claims_hosp

claims_surgery

claims_treat

claims_outpatient

claims_advanced

claims(t)

net_cf

0

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

−71,250.00

1

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

+2,728.26

2

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

+2,706.68

3

120.02

7.32

0.00

2.34

0.00

0.00

0.00

129.68

+2,554.93

4

119.05

7.26

0.36

2.50

1.19

0.11

0.08

130.55

+2,532.47

5

118.10

7.20

0.71

2.65

2.36

0.22

0.16

131.39

+2,510.20

The claims(t) column above is the benefit total, shown here so that the row can be read; it is not a column of the published statement. result_cf() publishes the split lines and no subtotal beside them, so that its columns add to net_cf as they stand — a statement carrying its own subtotal among its parts stops being additive unless the reader knows which column to skip. The total remains available as the claims(t) cells with its kind omitted.

The row for t = 5 is the one to check a rounding convention against: its seven displayed components re-add to 131.40 while claims(t) is 131.39, because the total is the sum of the unrounded lines. Assert against the unrounded values, not against the printed row.

Trace, month 0. pols_healthy(0) = 1, pols_cancer(0) = 0. Premium = 3,000 × 1 = 3,000.00. cover(0) = 0, so every cancer term is zero — not small, zero. expenses = 250 (maintenance) + 20,000 (acquisition) = 20,250.00 and claim_expenses = 0, because there are no claim events. commissions = 1.5 × 36,000 = 54,000.00. net_cf(0) = 3,000.00 − 20,250.00 − 0 − 54,000.00 = −71,250.00. Decrements: pols_healthy(1) = 1 × (1 − 0.0000792012) × (1 − 0.0078284203) = 0.992093; pols_cancer(1) = 0; Z(1) = 1 (the in-situ ledger cannot move before t = 3).

Trace, month 1. premiums = 3,000 × 0.992093 = 2,976.2790; expenses = 250 × 0.992093 = 248.0232 and claim_expenses = 0; commissions = 0 (renewal commission starts at t = 12); net_cf(1) = 2,976.2790 − 248.0232 = +2,728.26. pols_healthy(2) = 0.992093 × 0.992093 = 0.984249. Month 2 is month 1 scaled again: premiums = 2,952.7456, expenses = 246.0621, net_cf(2) = +2,706.68, pols_healthy(3) = 0.976466.

Trace, month 3 — cover attaches. cover(3) = 1 for the first time and the model starts paying, from a diagnosed population that is still empty: diag_first(3) = 0.976466 × 0.000122909 = 0.000120016, so claims_diag(3) = 1,000,000 × 0.000120016 = 120.0161. insitu_ev(3) = 0.976466 × 1 × 0.0000149949 = 0.0000146420, so claims_insitu(3) = 500,000 × 0.0000146420 = 7.3210 and the in-situ surgery is 0.80 × 200,000 × 0.0000146420 = 2.3427 — which is the whole of claims_surgery(3), because pols_cancer(3) = 0. Every other claim line is zero for the same reason. claims(3) = 120.0161 + 7.3210 + 2.3427 = 129.6798. expenses = 250 × 0.976466 = 244.1165 and claim_expenses = 5,000 × (0.000120016 + 0.0000146420) = 0.6733, ¥244.7898 of expense between them. net_cf(3) = 2,929.3982 − 129.6798 − 244.1165 − 0.6733 = +2,554.93. Decrements: pols_healthy(4) = (0.976466 − 0.000120016) × 0.992093 = 0.968626; pols_locked(4) = 0.000120016 × (1 − 0.0077050451) = 0.000119091, and unlock is zero because t + 1 < C. Z(4) = 1 × (1 − 0.0000149949) = 0.999985.

Trace, month 4 — the diagnosed state is live. pols_cancer(4) = 0.00011909, and the five care benefits are that number times the per-diagnosed-life-month amounts above: claims_hosp = 3,000.00 × 0.000119091 = 0.3573; claims_treat = 100,000 × 0.10 × 0.000119091 = 1.1909 (M(4) = 0, so paid_months = min(0.10, 60) = 0.10); claims_outpatient = 916.6667 × 0.000119091 = 0.1092; claims_advanced = 0.001 × (600,000 + 60,000) × 0.000119091 = 0.0786. claims_surgery now has both limbs: 200,000 × (0.35 × 0.0208333 × 0.000119091 + 0.80 × 0.0000145242) = 200,000 × (0.00000086837 + 0.0000116193) = 2.4975, where insitu_ev(4) = 0.968626 × 0.999985 × 0.0000149949 = 0.0000145242. diag_first(4) = 0.968626 × 0.000122909 = 0.000119053 gives claims_diag = 119.0525, and diag_rep(4) = 0 because pols_open(4) = 0. claims(4) = 119.0525 + 7.2621 + 0.3573 + 2.4975 + 1.1909 + 0.1092 + 0.0786 = 130.5481. premiums(4) = 3,000 × 0.968626 = 2,905.8782 — note that it is pols_healthy, not pols_if: the 0.000119 of diagnosed lives pay nothing. expenses = 250 × 0.968745 = 242.1863 — the maintenance expense is on pols_if, because a waived policy is still serviced — and claim_expenses = 5,000 × (0.000119053 + 0.0000145242) + 3,000 × 0.0208333 × 0.000119091 = 0.6679 + 0.0074 = 0.6753, ¥242.8616 of expense between them. net_cf(4) = 2,905.8782 − 130.5481 − 242.1863 − 0.6753 = +2,532.47.

Policy year 1 in aggregate (t = 0…11, all at age 40, all in policy year 1 — the strongest single test target in this file, because it exercises the waiting-period boundary and the first three months of the diagnosed state on one set of rates).

Line

Policy year 1 total

premiums

34,462.5629

claims_diag

1,046.0977

claims_insitu

63.8082

claims_hosp

12.3980

claims_surgery

26.4454

claims_treat

41.3265

claims_outpatient

3.7883

claims_advanced

2.7275

claims(t) total

1,196.5915

expenses

22,872.9134

claim_expenses

6.1269

commissions

54,000.0000

net_cf

−43,613.0689

with Σ pols_if(t) = 11.491654, Σ pols_healthy(t) = 11.487521, Σ pols_cancer(t) = 0.004133, and at the year end pols_if(12) = 0.909137, pols_healthy(12) = 0.908130, pols_cancer(12) = 0.001006, M(12) = 0.4002, V(12) = ¥2,401.31 and Z(12) = 0.999865. (The totals are sums of unrounded monthly values; the six displayed monthly rows do not re-add to them.)

What the numbers say. Year-1 claims are 3.47% of year-1 premium, against 21.5% on the medical chassis at the same age, same daily amount basis and same expense scale — and the gap is the product, not an error. Three things drive it. The first quarter pays nothing. The diagnosed population starts empty and is still only 0.11% of the in-force after twelve months, so the five benefits that run on it — at ¥16,035 per diagnosed life-month — contribute 16,035 × 0.004133 = ¥66.27 in the whole year, and of the ¥26.45 of surgery benefit ¥20.42 is in-situ surgery, which is not on that state at all. And cancer incidence at 40 is 0.00147 a year against the medical chassis’s 0.0466 hospitalisation incidence — a factor of 32 — while the sourced incidence curve rises by a factor of 11.3 from the 40–44 band to the 85–89 band (220.28 to 2,497.39 per 100,000 R5). This is a product whose cost is almost entirely in front of it: the ¥74,000 of acquisition expense and initial commission at t = 0 is recovered from an early margin that the incidence curve then takes back with interest. A ten-year projection — the horizon the 1号収支分析 REG-R22 and the third-sector ストレステスト R3 both use — sees almost none of the liability this contract actually carries.

Valuation and reserve pointers#

This library projects gross cash flows. Every valuation layer below consumes them and is cited, never reproduced. The statutory chain is the third-sector chain and is set out once, on the chassis, in the medical technical notes (医療保険); only what differs for cancer is repeated here.

  • 標準責任準備金. 保険業法 第116条 requires the reserve and delegates the method REG-R4, 施行規則 第68条 fixes scope REG-R7, and 平成8年大蔵省告示第48号 sets it as net level premium (heijun jun-hokenryō-shiki, 平準純保険料式) on the standard valuation interest rate (hyōjun riritsu, 標準利率) and the standard table R4 REG-R10; for contracts from 1 April 2018 that table is 第三分野標準生命表2018 R1 R2 REG-R11 REG-R18. The 標準利率 in force could not be established from a retrieved document and any value asserted for it is unverified REG-R10. What the chain does not contain is a cancer-incidence basis: the reserve’s morbidity assumption is the insurer’s own, unpublished R3 REG-R2.

  • 危険準備金, third-sector limb. 施行規則 第69条 carries the reserve taxonomy REG-R8; the 監督指針 requires the limb be computed under the ストレステスト of 平成10年6月8日大蔵省告示第231号 with a 負債十分性テスト, reflecting the uncertainty that 保険事故発生率 deteriorates, in principle per 契約区分 sharing a common 基礎率 R4 REG-R13 REG-R14. The FSA policy paper puts the stress at 危険発生率A covering 99% of incidence risk and 危険発生率B 97.7%, over a 10-year horizon, with annual 事後検証 R3; the notification itself was not retrieved and its magnitudes are unverified REG-R13. jplib implements the capability the regime demands — a re-runnable incidence basis, parameterized so a shock can be applied per grouping — and not the statutory stress. That distinction must not be blurred.

  • ESR, and 1号収支分析. From 31 March 2026 insurers are supervised on 経済価値ベースの ソルベンシー規制: 現在推計 + MOCE at each 基準日 on assumptions re-set then, required capital at 99.5%, corrective action below 100% REG-R15, superseding the ソルベンシー・マージン比率 200% trigger REG-R17. jplib computes neither; what it owes both is a projection re-runnable at a stated 基準日. The appointed actuary (hoken keirinin, 保険計理人) of 保険業法 第120条 REG-R5 submits the 意見書 of 第121条 REG-R6, which the 実務基準 turns into a forward income-and-outgo analysis over 「少なくとも将来10年間」 by 区分経理 segment REG-R22 — and on this product more than any other, ten years is a small fraction of the liability. J-GAAP REG-R10, ESR REG-R15 and IFRS 17, voluntary in Japan REG-R47, are three measurement bases fed by one set of cash flows, which is why these stay undiscounted.

  • Not applicable to this chassis. 契約者配当 and the surplus-distribution methods of 施行規則 第30条の2 REG-R9 do not attach: the composite is 無配当 [S5] [S6] [S11]. 価格変動準備金 under 第115条 is asset-driven and outside a liability projection REG-R3.

  • Policyholder tax, not modelled. The premium falls in the 介護医療保険料控除 basket of the post-2012 生命保険料控除 R8 REG-R43; the anchor’s ¥36,000 annual premium sits in the second income-tax band for a deduction of ¥28,000 = ¥36,000 × 1/2 + ¥10,000 R9. Benefits are stated to be in principle non-taxable where the payee is the insured, a spouse, a lineal relative or a 生計を一にする親族 [S1], and are not projected net of policyholder tax.

Key sensitivities and model risks#

In rough order of leverage on a cancer block:

  1. The survival basis, not the incidence basis, is the biggest lever — and it is the one a medical model does not have. Three of the seven benefit streams (repeating diagnosis, unlimited-day inpatient, monthly treatment) are integrals over post-diagnosis survival. The base run’s flat excess hazard from a 5-year relative survival figure R6 is a std construction that overstates late-duration mortality, and every month of survival it removes takes benefit the product is designed to pay with it. A cure-fraction or duration-banded hazard moves the liability in one direction only: up.

  2. The relapse hazard. rel_rate = 0.06 p.a. std produces 1.4856 diagnosis payments per diagnosed life at the anchor age. There is no source. Doubling it to 0.12 p.a. moves the diagnosis benefit by more than any other single parameter, and the repeat_conditioned switch [S7] [S10] moves it by an order of magnitude in the other direction.

  3. The incidence basis is genuinely sourced — and that makes its remaining std parts sharper, not softer. The age-band rates are public and citable R5 REG-R29; the sex split is a two-point interpolation, and the male and female curves cross, so a unisex or badly split basis is wrong at every age R5. The in-situ increment’s age-invariance is std and is the second-order version of the same problem.

  4. The treatment benefit’s frequency, and the 60-month cap. treat_prob = 0.10 std with no observed range gives 12.98 expected qualifying months against a 60-month cap [S5] [S11]. Because the cap binds for a real minority rather than never, the deterministic cohort-average ledger’s understatement of E[min(Σ, K)] is a live error here, not the dormant one it is on the medical chassis.

  5. Longevity, not mortality, is the tail risk — twice over. The sourced incidence curve rises by a factor of 11.3 from the 40–44 band to the 85–89 band R5, so the liability is concentrated where the survival assumption is least certain; and on top of that a lighter mortality basis keeps more lives in the diagnosed state, where they are drawing ¥16,035 a month at the anchor cell’s parameters. Using the valuation table unadjusted as a best estimate is a conservative error in the reserving direction and a material one over a 76-year projection R2 REG-R20.

  6. The waiver makes premium and claims anti-correlated by construction. Every first diagnosis simultaneously starts the benefit stream and stops the premium [S10] [S11], and a diagnosed life then cannot lapse. Any error in incidence therefore hits both sides of the cash flow at once, roughly doubling its effect on net_cf.

  7. The premium is an input with no market anchor. No carrier publishes a rate table for this product; the only retrieved price point is a 2013-basis ten-year term at twice the composite’s benefit amounts [S5], and the 算出方法書 is not published REG-R2. Every profitability statement about the anchor cell is a statement about ¥3,000 std, not about the market.

  8. Expense inflation on a small premium. ¥250 a month of maintenance against a ¥3,000 premium is 8.3% of premium, the premium is fixed for life, and the expense is not — and on the waived population the expense runs with no premium against it at all.

Known modeling pitfalls#

  • The 90-day waiting period is a hard zero, not a reduced rate. No cancer benefit of any kind is payable in months 0, 1 and 2, and no life transitions into the diagnosed state [S1] [S5] [S6] [S10] [S13]. A model that starts the incidence at t = 0 pays three months of benefit that no contract in the retrieved set pays.

  • The premium is still charged during the waiting period. Five carriers charge from inception [S1] [S5] [S6] [S7] [S10]; one charges nothing for three months and says explicitly that this is not a discount [S11]. The composite charges. Suppressing the premium and the benefit together is a different product.

  • An in-window diagnosis voids the contract; it does not lapse it. Premiums already collected come back [S1] [S5] [S10]. Putting it in the lapse column keeps premium income the insurer never earned. The base run omits the adjustment and the omission is 0.037% of policies at the anchor cell — state it, do not silently absorb it.

  • 上皮内新生物 is a second benefit tier, not a discount on the first. It has its own once-only cap, it is not payable after a full-rate benefit, it does not start the two-year cycle, and it does not trigger the premium waiver [S6] [S11] [S7] [S10]. Implementing it as insitu_pct × claims_diag inside the main diagnosis benefit gets the amount right and the cap, the cycle and the waiver all wrong.

  • Premiums are weighted by pols_healthy, claims by pols_cancer. The waiver fires on the same event that starts every benefit [S10] [S11]. Multiplying the premium by pols_if is the single largest arithmetic error available in this product, and it is invisible in the first three months because the two are equal.

  • A diagnosed life cannot lapse. No premium to miss and no surrender value to take [S7] [S10] [S11]. Applying the healthy lapse rate to the diagnosed state deletes exactly the claimants the product exists to pay.

  • There is no L1, no LA and no benefit-driven termination. Inheriting medical’s 60/120-day per-hospitalization cap, its 1,095-day aggregate or the termination they create caps a benefit that every source says is uncapped [S1] [S3] [S5] [S6] [S10] [S13] R11, and it terminates a contract that cannot exhaust [S1].

  • The 2-year cycle is not the 180-day one-hospitalization rule. Different length, different trigger (a payment, not a discharge), different consequence (eligibility, not grouping) [S5] [S1]. Sharing one clock between medical and cancer breaks both.

  • The cycle clock runs from the previous trigger, not the previous payment or admission. The three sourced two-year designs measure it from the trigger date [S5], from the first day of the calendar month of the previous payment [S7], and from the start date of the last hospitalisation [S10]. Only the first needs no second date carried alongside; implementing one and documenting another is a silent divergence.

  • The treatment benefit’s unit is a month, not a day and not an event. A prescription covering two months pays one month; two triggers in one month pay once; two triggers on one day pay once [S10] [S11]. Any formula in which a day count reaches claims_treat is wrong by construction, and the dimensional check above is there to catch it.

  • The 60-month cap is a ledger on months, and the ledger is per diagnosed life. Weighting it by pols_cancer measures the block’s consumption, not the individual’s, and defers the cap forever. Diluting it with diag_rep as well as diag_first resets a ledger that should keep running: a repeat trigger is an already-diagnosed life.

  • Do not delete a ledger because it reads small. M(12) = 0.4002 months and V(12) = ¥2,401.31 at the anchor cell, but E[min(Σ, K)] ≠ min(E[Σ], K), and unlike medical’s 通算 day ledger this one is reached by a real minority of diagnosed lives.

  • In-situ diagnoses generate the surgery benefit and nothing continuing std. They do not enter pols_cancer, so they contribute no inpatient, treatment or outpatient benefit — a documented simplification with a stated direction of error, not an omission. A model that routes them into the diagnosed state credits them with an exposure 患者調査 does not measure R7.

  • claims_lapse(t) is identically zero and claims_death(t) does not exist. There is no surrender value under 終身払 [S7] [S10] [S11] and no death benefit in the composite [S1]. A non-zero column for either is a benefit the contract does not have.

  • 第三分野標準生命表2018 is a valuation table, not experience. Using it unadjusted as a best-estimate decrement understates mortality, which on a morbidity product overstates the liability; the std 1.25 factor unwinds the sourced 70–85% adjustment band and nothing more R2 REG-R20. The same factor must be used here and on the medical chassis.

  • Relative survival is not a mortality table. R6 publishes 5年相対生存率, which nets out background mortality — so it converts into an excess hazard added to the baseline, not into a replacement for it. Multiplying survivorship by a relative-survival figure double-counts the background.

  • Cancer deaths sit on both sides of the mortality basis. The never-diagnosed carry a population table that already contains cancer mortality, and the diagnosed carry it again as an excess hazard. At the anchor age the effect is 1% of the excess hazard; at 80 it is not. A net_of_cancer baseline is a switch, and the double-count must be stated rather than discovered.

  • Age-band incidence steps; it does not glide. The registry publishes five-year bands R5. Interpolating within a band is a choice, not a correction, and it must be the same choice in the model and in the CSV’s provenance column.

  • 復活 re-runs the waiting period. A reinstated cancer policy has 90 days of no cover in front of it [S1] [S6]. Modelling reinstatement as a negative lapse restores cover the contract does not restore, and it deletes a real anti-selection control.

  • Rounded lines do not re-add. The t = 5 claim components displayed to ¥0.01 sum to 131.40 against a claims(t) value of 131.39, and the seven policy-year-1 claim lines displayed to four decimals sum to 1,196.5916 against a claims(t) total of 1,196.5915. Assert against the unrounded aggregation, never against a sum of displayed figures.

  • A subtotal published beside its own parts. The benefit total is a cells, never a column: result_cf() carries the nine claims_* splits and nothing named claims, so its columns add to net_cf as they stand. Publishing the total alongside them makes the statement silently non-additive for any reader who sums the row, and doubles the benefit side of every check written off the table.