The Projection Space

The by-policy projection of the Cancer_JP_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 month beginning at the 契約日 and t = proj_len() - 1 the last month of cover. Cover is whole of life, so proj_len() = 12 x (omega_age() - issue_age() + 1) — 924 months on the anchor cell. There is no maturity benefit, no 満期保険金 and no benefit-driven termination: paying the diagnosis lump sum neither ends nor exhausts the contract, and with no day limits the inpatient benefit cannot exhaust it either. The decrements are death and lapse, and nothing else.

Input data

Inputs are external files: plain CSVs living in the model folder’s parent directory, products/cancer/, read at run time rather than stored inside the model. The model folder therefore holds nothing but formulas — no _data/, no IOSpec, no embedded values — so a diff of the model shows logic changes only, and an input can be edited or swapped without rewriting the model. This follows annuallife.TradLife_A; contrast basiclife.BasicTerm_S, which keeps its inputs inside the model through modelx’s IOSpec machinery.

The consequence worth knowing: the model is not portable on its own. Copying the Cancer_JP_S folder without its parent’s CSVs produces a model that reads and then fails on first evaluation.

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
incidence_table_file	data.incidence_table()	incidence_table.csv
sex_factor_file	data.sex_factor_table()	sex_factor_table.csv
survival_table_file	data.survival_table()	survival_table.csv
lapse_table_file	data.lapse_table()	lapse_table.csv
hosp_stay_file	data.hosp_stay_table()	hosp_stay_table.csv

Naming

Cells names follow lifelib’s basiclife.BasicTerm_S wherever that model has an analogue — pols_* for policy counts, plural nouns for cash flows, *_rate for annual rates and *_rate_mth for their monthly counterparts, claims(t, kind) with an uppercase kind string. The technical notes use compact symbols instead. The mapping is:

Notes symbol	Cells	Meaning
(model point row)	model_point()	The selected model point
t	(the cells argument)	Policy month, 0-based
x	issue_age()	契約年齢 (満年齢) at issue
age(t)	age(t)	Attained age x + t//12
y(t)	policy_year(t)	Policy year, 1-based
(terminal age)	omega_age()	116 male / 118 female
(horizon)	proj_len()	Months projected
W	wait_months()	Waiting period in months
cover(t)	cover(t)	1 from t >= W, else 0
A	base_amount()	基本給付金額
DB	diag_benefit()	がん診断一時金, 100 x A
u	insitu_pct()	上皮内新生物 grading of DB
D	daily_amount()	がん入院給付金日額
m_s	surg_mult()	Surgery multiple of A
B_tr	treat_benefit()	がん治療給付金 per month
K	treat_cap()	Lifetime cap in months
(outpatient rate)	outp_daily()	がん通院給付金日額
C	cycle_months()	Repeat cycle in months
(payment period)	prem_period_type()	終身払 or 65歳払済
P	premium_mth_pp()	Monthly office premium
(band rate)	inc_rate_both(t)	罹患率 of the age band
f_male(a)	sex_factor(a)	Male / both-sexes factor
inc_rate(age, sex)	inc_rate(t)	Annual first-diagnosis rate
i(t)	inc_rate_mth(t)	Monthly incidence
iz(t)	insitu_rate_mth(t)	Monthly 上皮内新生物 incidence
(table rate)	mort_rate_at_age(a)	第三分野2018 proxy at age a
mort_rate(age)	mort_rate(t)	Annual best-estimate q
q(t)	mort_rate_mth(t)	Monthly q, never diagnosed
S5	surv_5y()	5年相対生存率
mu_ex	mu_ex()	Annual excess hazard
q_c(t)	mort_rate_canc_mth(t)	Monthly q, diagnosed
(table)	lapse_rate(t)	Annual lapse rate
w(t)	lapse_rate_mth(t)	Monthly lapse, healthy
w_c(t)	lapse_rate_canc_mth(t)	Monthly lapse, diagnosed
w_cum(t)	lapse_cum(t)	Cumulative lapse share
lam	sel_lapse_lambda	Anti-selective loading
r	relapse_rate_mth(t)	Monthly relapse hazard
sc(t)	surv_canc(t)	Diagnosed survival factor
(void rule)	void_prob()	In-window voidness
(initial exposure)	pols_if_init()	In force at t = 0
pols_healthy(t)	pols_healthy(t)	Never diagnosed
pols_locked(t)	pols_locked(t)	Diagnosed, cycle running
pols_open(t)	pols_open(t)	Diagnosed, cycle expired
pols_cancer(t)	pols_cancer(t)	locked + open
pols_if(t)	pols_if(t)	healthy + cancer
(intra-month timing)	pols_if_at(t, timing)	In force at a named point
diag_first(t)	diag_first(t)	First diagnoses
diag_rep(t)	diag_rep(t)	Repeat triggers
trig(t)	trig(t)	All payment triggers
unlock(t)	unlock(t)	Cycle expiries arriving
insitu_ev(t)	insitu_ev(t)	上皮内新生物 diagnoses
Z(t)	insitu_avail(t)	Once-only tier unused
(consumed)	insitu_used(t)	Once-only tier consumed
(decrement)	pols_death(t)	Deaths, both states
(decrement)	pols_lapse(t)	Lapses, both states
h	hosp_rate_mth(t)	Monthly admissions
L	hosp_stay_days(t)	Mean stay in days
s_h, s_z	surg_per_hosp, surg_per_insitu	Surgeries per event
p_tr	treat_prob	Qualifying-month chance
M(t)	treat_months(t)	Treatment-month ledger
(capped draw)	paid_months(t)	Months paid in month t
o	outp_days	Outpatient days per year
f_a	adv_freq_mth()	Monthly 先進医療 frequency
S_a	adv_sev	Mean 技術料
LV	adv_cap	先進医療 lifetime cap
V(t)	adv_paid(t)	先進医療 ledger
pay(t)	adv_pay(t)	先進医療 draw in month t
P x pols_healthy	premiums(t)	Premium income
(claim lines)	claims(t, kind)	Benefit outgo by kind
e(t)	maint_expenses(t)	Maintenance expense
ec_d, ec_h	claim_expenses(t)	Claim handling expense
E0, e(t)	expenses(t)	Acquisition + maintenance
(commission)	commissions(t)	Commission outgo
net_cf(t)	net_cf(t)	Net cash flow, income +

Five names needed care.

pols_if_at(t, timing) carries the library-wide "BEF_DECR" / "BEF_LAPSE" / "AFT_DECR" vocabulary, and "BEF_LAPSE" is the sum over the two states, each decremented on its own mortality basis — a blended rate on pols_if does not reproduce it. What the vocabulary cannot show here is the movement that defines the product: the three timings are decrement timings, and a first diagnosis is not a decrement. diag_first() moves a life from pols_healthy() to pols_cancer() before the decrement, changing which benefits and which premium the life carries while leaving pols_if identical at all three points. Read pols_healthy(), pols_cancer() and diag_first() for the state movement; pols_if_at answers only how many lives are left, never which state they are in.

pols_open is the population eligible for a repeat payment, not the population in payment. The two-year cycle is a clock keyed to an event — the previous payment trigger — so the flow out of pols_locked is a 24-month delay, not a rate: unlock() is the trigger cohort of month t - C carried forward on diagnosed decrements alone. This clock is emphatically not the 180-day one-hospitalization memory of the medical chassis: different length, different trigger, different consequence, and sharing one clock between the two products breaks both.

insitu_ev is a second benefit tier, not a discount on the first. It attaches to pols_healthy() alone, carries its own once-only ledger insitu_avail(), does not move the life into the diagnosed state, does not start the two-year cycle and does not trigger the premium waiver. Implementing it as insitu_pct x claims_diag inside the main diagnosis benefit gets the amount right and the cap, the cycle and the waiver all wrong.

treat_months and adv_paid are ledgers per diagnosed life, not per block. They measure what an individual has consumed against the 60-month and ¥20,000,000 caps, so they are carried as a cohort average diluted by new entrants — and only by diag_first(), because a repeat trigger is an already-diagnosed life whose ledgers continue. Weighting them by pols_cancer would measure the block’s consumption and defer the cap forever; diluting them with diag_rep() would reset a ledger that should keep running.

claims(t, "LAPSE") exists and returns zero. There is no surrender value at any duration under 終身払, so a lapse is a pure decrement that pays nothing; a column of zeros states the product fact where a missing column would only hide it. There is no claims_death at all, because the composite carries no death benefit — mortality is a pure liability-releasing decrement.

Three states, and why two will not do

The medical chassis projects one in-force population and reads a hospitalisation incidence off it. Here 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. The model therefore carries pols_healthy(), pols_locked() and pols_open(), and needs a survival basis as well as an incidence basis. The single roll-forward that ties them together is

pols_cancer(t+1) = ( pols_cancer(t) + diag_first(t) ) x sc(t)

which check_cancer_roll_fwd() asserts against the separate locked / open recursions in every projected month.

The waiting period is a hard zero

cover() 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. It is a hard zero, not a reduced rate: a model that starts the incidence at t = 0 pays three months of benefit that no contract in the retrieved set pays, and one that suppresses the premium along with the benefit is a different product.

Premiums ride on pols_healthy, claims on pols_cancer

The waiver fires on the same first invasive diagnosis that starts every benefit, so the premium stream is carried by the never-diagnosed sub-population alone and the two weights are disjoint. 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. pols_payer() is where the choice is made, and it is a product choice: on the waiver_trigger = "none" and "disability" designs the diagnosed keep paying and can lapse, which is why lapse_rate_canc_mth() is not simply zero.

Dimensions

D x hosp_stay_days is JPY per admission, so the inpatient benefit is D x L x h x pols_cancer. B_tr is JPY per month, so the treatment benefit is B_tr x p_tr x pols_cancer directly — no day count enters it at all, and inserting one is the commonest way to break this product. The medical chassis’s benefit is 日額 x days and this product’s central benefit is 月額 x months; the two have different dimensions and cannot share a formula.

Modules that are off in the base run

Eight of the notes’ optional constructions are implemented and held at an inert base value, so that the base run reproduces the worked example while the machinery stays visible and testable:

• The validity adjustment, void_adjust. A diagnosis inside the 90-day window makes the contract void, not lapsed: the policy was never in force, so the premium already collected comes back with the future benefit. void_prob() is that probability — 0.037% of policies at the anchor cell — and switching void_adjust on scales pols_if_init() down by it, which releases premium and benefit together at outset. The acquisition expense and initial commission are not scaled: they were incurred.

• Anti-selective lapse, inc_eff = inc_rate (1 + lam max(0, w_cum - w_ref)), with sel_lapse_lambda = 0. Healthy lives lapse first, so the persisting never-diagnosed block is progressively impaired on the incidence basis. On this product the effect is amplified by the waiver: the healthiest lives are also the only ones still paying. No Japanese evidence was retrieved.

• Conditioned repeats, the repeat_conditioned model-point flag. Two of the three sourced two-year designs require the insured to be under treatment for the second and later payments; the flag multiplies the relapse hazard by treat_prob, so the two designs differ by an order of magnitude, not by a rounding. False on the anchor cell, true on model point 3.

• The age gradient on the mean stay, hosp_age_gradient. The 14.4-day all-ages figure and the 35-64 / 65+ / 75+ gradient are both sourced, but the gradient is published on four broad bands and the incidence on twenty-one narrow ones, so the base run takes the all-ages figure.

• The 保険年齢 age offset, mort_age_offset. 第三分野標準生命表2018 is constructed for use on a nearest-birthday basis, so reading it at 満年齢 understates the valuation age by about half a year. Set the offset to 0.5 to read at age(t) + 0.5, interpolating between rows.

• A cancer-free mortality baseline, net_of_cancer. The never-diagnosed carry a population table that already contains cancer deaths and the diagnosed carry them again as an excess hazard. At the anchor age the double count is 1% of the excess hazard; at 80 it is not. cancer_death_share = 0.28 is a [std] placeholder with no observed range — no document in this product’s source set gives 悪性新生物’s share of all-cause Japanese mortality — so the switch demonstrates the capability rather than a calibration.

• Repricing at renewal, renew_reprice_rate, on the 10年更新 定期 chassis flag. The renewal reprices at then-current rates, which would ordinarily close the contract boundary at each renewal; the base run holds the issue rate flat and records the tension rather than resolving it. Model point 3 carries the flag with the rate at zero.

• The diagnosed lapse loading, lapse_canc_factor = 1.0. It scales the diagnosed lapse rate off the healthy one, and its base value is inert rather than off: wherever the waiver fires a diagnosed life has no premium to miss and no surrender value to take, so lapse_rate_canc_mth() returns zero whatever the factor is. It reaches a cash flow only on the waiver_trigger = "none" and "disability" designs — model point 7.

Two further constructions the notes name are deliberately not implemented, and the absence is stated rather than left to inference. A duration-banded excess hazard needs cohort tracking by time since diagnosis that the three-state model does not carry, and the grace-period lag and 復活 are modelled as a new model point rather than as a negative lapse, because the 90-day waiting period re-runs from the 復活日.

One divergence from the technical notes

The notes carry disch_rider as a model point attribute but their cash-flow section does not define the がん退院一時金 benefit, so claims() (t, "DISCHARGE") supplies a [std] formula built from product-spec.md instead: disch_mult x A per qualifying discharge, on the disch_qual_share of admissions whose stay reaches the contractual ten days. The 30-day re-payment bar is not modelled — at 0.0208 admissions per diagnosed life-month the overlap is second-order. The rider is off on every model point but 8, so the base run and the worked example are untouched by it; see model.md.

Sign convention

The notes’ net_cf(t) is already income positive — premiums less claims, expenses and commission — which is the library-wide sign of net_cf(), so there is no outgo-positive liability_cf companion to publish: one stream, one sign, one name.

What the shape of the answer is

Year-1 claims are 3.47% of year-1 premium at the anchor cell, against 21.5% on the medical chassis at the same age and expense scale, and the gap is the product rather than an error: the first quarter pays nothing, the diagnosed population starts empty and is still 0.11% of the in-force after twelve months, and cancer incidence at 40 is a factor of 32 below the medical chassis’s hospitalisation incidence. This is a product whose cost is almost entirely in front of it — the sourced incidence curve rises by a factor of 11.3 from the 40-44 band to the 85-89 band — so a ten-year projection sees almost none of the liability the contract actually carries.

Cells Descriptions

model_point()

The selected model point as a Series.

policy_id()

The policy identifier of the selected model point.

chassis()

The cover chassis: shushin (終身) or teiki (10年更新 定期).

終身 is the composite because four of the seven retrieved carriers write it, against a ten-year renewable term at two and a five-year one at the expense carrier. The 定期 flag carries automatic renewal with benefit history, waiver history and 責任開始期 continuous across the renewal, so the projection horizon is unchanged; what the renewal really does is reprice, and that is the renew_reprice_rate switch.

issue_age()

x: the 契約年齢 at issue, on a 満年齢 basis, in the composite’s 20-75 range.

満年齢 is the attained age at the 契約日 with the fraction discarded, incremented at each 年単位の契約応当日. 第三分野標準生命表2018 is constructed for use on a 保険年齢方式 (nearest-birthday) basis, so reading it at 満年齢 understates the valuation age by about half a year; the base run accepts the offset [std] and mort_age_offset is the switch that removes it.

sex()

The sex (M / F) of the insured.

A unisex basis would be materially wrong at every age on this product, because the male and female incidence curves cross: female incidence is nearly three times male at 35-39 and half of it at 70-74.

base_amount()

A: the 基本給付金額, the amount every benefit in the composite is a multiple of.

The only published course menu is ¥5,000 and ¥10,000; ¥10,000 is the composite default because it is the amount at which the published multiples and the published ¥1,000,000 headline diagnosis benefit are mutually consistent.

diag_benefit()

DB: the がん診断一時金, 100 x A = ¥1,000,000 on the anchor cell.

Payable on the first diagnosis of an 悪性新生物 on or after the がん責任開始日 and again on each fresh 再発 / 転移 / 新生 once the cycle has expired, with no lifetime cap and no termination on payment.

cycle_months()

C: the repeat cycle in months, measured from the previous payment trigger.

At most one diagnosis payment in any two years. The three sourced two-year designs measure the clock from the trigger date, from the first day of the calendar month of the previous payment, and from the start date of the last hospitalisation; only the first needs no second date carried alongside, and it is the one modelled.

insitu_pct()

u: the 上皮内新生物 grading of the diagnosis benefit, in {1.00, 0.50, 0.10}.

The three sourced treatments of in-situ disease — full rate, half rate and 10% — are a single model-point parameter. Whatever the grading, the benefit is payable once, on its own cap, is not payable after a full-rate benefit, and does not trigger the premium waiver.

daily_amount()

D: the がん入院給付金日額, equal to A in the composite.

Paid per day of a cancer hospitalisation with no per-hospitalization day limit and no 通算 lifetime limit — the structural difference from the medical chassis, whose 60 or 120-day and 1,095-day ledgers dominate its model.

surg_mult()

m_s: the がん手術給付金 as a multiple of A, 20 on the composite.

Unlimited count; simultaneous procedures count as one. Payable in full on 上皮内新生物 as well, which is why claims() (t, "SURGERY") has two limbs.

treat_benefit()

B_tr: the がん治療給付金 per qualifying calendar month, 10 x A on the composite.

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. Any formula in which a day count reaches this benefit is wrong by construction.

treat_cap()

K: the lifetime cap on the monthly treatment benefit, in months.

60 at the two carriers that write the benefit. At treat_prob and the diagnosed state duration implied by the survival basis, a life diagnosed at the anchor age accumulates an expected 12.98 qualifying months against it, so the cap binds for a long-course minority — which is what a 60-month cap is for, and why treat_months() cannot be dropped as immaterial.

outp_daily()

The がん通院給付金日額, equal to A in the composite.

Treatment-linked — attendance for surgery, radiation, thermal therapy or non-oral chemotherapy, not attendance for follow-up — and with no day limit. Not payable for a day of attendance during a stay for which the inpatient benefit is paid.

wait_months()

W: the 90-day waiting period expressed on the monthly grid, 3 months.

がん責任開始日 is the 91st day counting the 責任開始日 as day 1 at five carriers; two write three calendar months instead. On a monthly grid these are the same boundary [std] and the model does not claim a precision it does not have.

prem_period_type()

The premium-paying period as a category: whole_life (終身払) or to_65.

Named prem_period_type and not prem_period because the library reserves prem_period for a duration in the model’s own grid unit; this returns one of two labels. The model point column keeps the name prem_period.

終身払 is the composite default and is the design under which no surrender value ever arises on any retrieved contract; the 短期払 variant is the only route by which this chassis acquires a surrender value at all, which the model does not carry either way.

premium_mth_pp()

P: the level monthly office premium per policy [std].

premium_mth_pp and not premium_pp: the library spells a monthly per-policy premium premium_mth_pp and an annual one premium_pp, and this product’s grid step is the payment interval, so the figure here is a month’s premium.

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 算出方法書 is a 基礎書類 filed with the 金融庁 and is not published, and for third-sector business there is additionally no standard incidence table and no reference pure premium to fall back on. The single retrieved price point is a ten-year term at twice the composite’s benefit amounts on a 2013 calculation basis; 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.

prem_mode()

The premium frequency; 月払 (monthly) throughout the composite.

Carried because the product documentation distinguishes 月払 / 半年払 / 年払, and inert on a monthly grid whose step is the payment interval. It is also why the 90-day waiting period lands exactly on a grid boundary.

waiver_trigger()

The 保険料払込免除 trigger: cancer_diag, disability or none.

cancer_diag is the composite: the waiver fires on the first 悪性新生物 diagnosis on or after the がん責任開始日, and 上皮内新生物 does not trigger it. The consequence runs through the whole model — premiums ride on pols_healthy(), and a diagnosed life has no premium to miss and no surrender value to take, so it cannot lapse. On the other two designs both of those reverse; see pols_payer() and lapse_rate_canc_mth(). The disability incidence itself is out of scope [std scope]: no basis for it appears in this product’s source set.

adv_rider()

Whether the がん先進医療特約 is attached.

A reimbursement of the 技術料 in full against a ¥20,000,000 lifetime cap, with a 10% cash top-up capped at ¥500,000 per 療養; the rider terminates when the cap is reached, which adv_pay() implements as a draw against adv_paid().

disch_rider()

Whether the がん退院一時金 rider is attached; false on the base run’s anchor cell.

¥100,000 on discharge from a covered stay of ten or more consecutive days. The technical notes carry the flag but not a formula for it, so the benefit is a [std] construction here; see the Space docstring and model.md.

repeat_conditioned()

Whether second and later diagnosis payments require the insured to be in treatment.

False in the composite, which does not condition the repeat. Two of the three sourced two-year designs do condition it — on being under treatment at one carrier and hospitalised at another — and the switch multiplies the relapse hazard by treat_prob, so the two designs differ by an order of magnitude.

omega_age()

The terminal age of 第三分野標準生命表2018: 116 male, 118 female.

The horizon of a whole-of-life projection, and the last age the shipped table carries: both terminal rates are sourced q = 1.00000 rows quoted from that table, so the projection ends where the published table ends rather than where a fitted curve happens to close.

proj_len()

The projection length in policy months: 12 x (omega_age - x + 1).

924 months on the anchor cell. Cover is whole of life with no maturity benefit and no benefit-driven termination, so the horizon is the mortality table’s and nothing shortens it — including the 定期 chassis flag, whose renewal is automatic.

age(t)

age(t): the attained 満年齢 in policy month t, x + t // 12.

policy_year(t)

y(t): the policy year containing month t, t // 12 + 1.

cover(t)

cover(t): 1 from the がん責任開始日, 0 inside the 90-day waiting period.

A hard zero, not a reduced rate. It multiplies every cancer benefit, the incidence transition and the in-situ transition, so in months 0, 1 and 2 the model pays nothing and transitions nobody — while still collecting the premium, because five of the six carriers that state it charge from inception.

mort_rate_at_age(a)

The shipped [std] mortality table rate at age a, which may be fractional.

A construction graduated between the individual 第三分野標準生命表2018 rates the library quotes and attributes — 男 q(40) = 0.00076 among them — and not a copy of that table; see the Data docstring. Every quoted rate is reproduced exactly at its own age; the ages between them are log-linear interpolations. A fractional age is linearly interpolated between the two bracketing rows, which is what mort_age_offset needs.

mort_rate(t)

The annual best-estimate mortality of a never-diagnosed life in month t.

mort_be_factor x q_third_sector(age(t), sex), capped at 1. 第三分野標準生命表2018 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, with a risk-theory adjustment bounded at 70% below and 85% above the unadjusted rate. mort_be_factor = 1.25 [std] is the reciprocal of 0.80, a round value inside that sourced band, so the factor unwinds the table’s stated margin and nothing more. The same factor must be used here and on the medical chassis. The cap binds at the terminal age alone, where the shipped table already carries the sourced q = 1.00000.

With net_of_cancer on, the rate is additionally netted of the [std] cancer share of deaths, so that the cancer mortality inside the table’s own rates is not carried twice once the diagnosed excess hazard is added.

mort_rate_mth(t)

q(t): the monthly mortality of a never-diagnosed life, 1 - (1 - q_ann)^(1/12).

surv_5y()

S5: the 5年相対生存率 of the insured’s sex, all sites, 2018 diagnoses.

63.17% male and 66.84% female. Relative survival, which already nets out background mortality — multiplying survivorship by it would double-count the background; it converts instead into an excess hazard, which is what mu_ex() does.

mu_ex()

mu_ex: the annual excess hazard of a diagnosed life, -ln(S5) / 5 [std].

0.0918681 per year for a male. 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 hazard would need cohort tracking by time since diagnosis that this three-state model does not carry, and it moves the liability in one direction only: up.

mort_rate_canc_mth(t)

q_c(t): the monthly mortality of a diagnosed life.

1 - (1 - q(t)) exp(-mu_ex / 12) — the baseline plus an excess hazard, not a replacement for it. 0.0077050451 at the anchor cell’s first year, which implies a mean diagnosed-state duration of 129.79 months and is what every one of the five care benefits is integrated over.

lapse_rate(t)

The annual lapse rate applying in policy year y(t) [std].

9 / 7 / 6 / 5.5 / 5 percent then a 4.5% plateau and a 3% ultimate, shared unchanged with the medical chassis so that the two third-sector products do not disagree about persistency. The only published industry-wide figure is a 5.6% 解約・失効率 measured on opening in-force sum assured, on a book dominated by death cover, which a がん保険 with no sum assured cannot enter; the shipped curve averages 5.5% over its first ten years against it. Policy years beyond the table take its last row.

lapse_rate_mth(t)

w(t): the monthly lapse rate of a never-diagnosed life [std].

1 - (1 - lapse_rate)^(1/12), applied after mortality at the end of the month. A lapse pays nothing: the composite is 無解約払戻金型 at every duration under 終身払, and with no surrender value neither 契約者貸付 nor 自動振替貸付 can operate, so a missed premium really does lapse the policy.

lapse_rate_canc_mth(t)

w_c(t): the monthly lapse rate of a diagnosed life; zero in the base run.

A product fact, not a refinement. The waiver fires on the first 悪性新生物 diagnosis, so a diagnosed life has no premium to miss, and there is no surrender value to cash in — so there is no mechanism by which a diagnosed policy leaves the book other than death. Applying the healthy lapse rate to the diagnosed state deletes exactly the claimants the product exists to pay. On the disability-trigger and no-waiver designs the premium does not stop, and the rate becomes the healthy one scaled by lapse_canc_factor.

lapse_cum(t)

w_cum(t): the cumulative lapse proportion of the never-diagnosed cohort before t.

A proportion of pols_if_init(), not a running total of lapse_rate_mth(), and it drives a loading on incidence rather than on lapse. Zero at t = 0.

sel_lapse_factor(t)

The anti-selective lapse loading on incidence in month t [std]; 1 in the base run.

1 + lam max(0, w_cum(t) - w_ref). Healthy lives lapse first, so the persisting never-diagnosed block is progressively impaired on the incidence basis. Off in the base run (sel_lapse_lambda = 0); no Japanese evidence for the loading was retrieved.

inc_band_at_age(a)

The five-year 全国がん登録 age band containing age a, as its starting age.

The registry publishes by five-year band, so the incidence steps and does not glide. Interpolating within a band is a choice, not a correction, and it would have to be the same choice in the model and in the CSV’s provenance column. The last row is the 100+ open band.

inc_rate_both(t)

The both-sexes 罹患率 of the age band containing age(t), per policy per year.

All sites C00-C96, crude rate, 2023 diagnoses, converted from the published per-100,000 figure. 220.28 per 100,000 at the anchor cell’s 40-44 band. This is the one assumption in the model that is genuinely sourced.

sex_factor(a)

f_male(a): the male / both-sexes incidence factor at age a [std].

Linear in age between the two sourced ratios, 0.551547 at the 35-39 band midpoint 37.5 and 1.377629 at the 70-74 band midpoint 72.5, and read at the band midpoint — so f_male(42.5) = 0.669559 serves the whole 40-44 band. The female limb is 2 - f_male, which is what makes the construction sum to twice the both-sexes rate.

The factor is clamped to [0, 2] [std], because outside that interval one limb of the construction goes negative and a negative incidence is not a rate. The clamp binds only on the 100+ band: the linear form reaches 2 at age 98.87, so at the 102.5 midpoint it would give a female rate of -0.086 x the band rate.

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. And the female limb does not reproduce the sourced female rates exactly — -1.2% at 35-39 and -6.1% at 70-74 — because the band rate 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, and it disappears the moment the by-sex grid from the same workbook replaces the construction.

inc_rate(t)

The annual first-diagnosis incidence per never-diagnosed policy in month t.

The band rate times the sex limb, times the anti-selective lapse loading. 0.00147490 per year on the anchor cell. For third-sector business the regulator states flatly that no standard incidence table 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 — and for cancer the public data is excellent, which is why only the sex split here is [std].

inc_rate_mth(t)

i(t): the monthly first-diagnosis incidence, inc_rate(t) / 12 [std].

Uniform within the band year; 0.000122909 per month on the anchor cell.

insitu_rate(t)

The annual 上皮内新生物 incidence per never-diagnosed policy.

insitu_share x inc_rate(t). The registry publishes paired rows with and without 上皮内がん — 993,469 invasive against 1,114,642 including in situ — an increment of 121,173 cases, 12.2% of the invasive count. The 12.2% is sourced; its age-invariance is [std] and is very likely wrong in a knowable direction, since in-situ detection is screening-driven and concentrated at the screened ages.

insitu_rate_mth(t)

iz(t): the monthly 上皮内新生物 incidence, 0.0000149949 on the anchor cell.

relapse_rate_mth(t)

r: the monthly relapse hazard once the cycle is open [std].

rel_rate / 12 = 0.005, with the deeming rule — a continuing hospitalisation at cycle expiry is a fresh trigger — folded into it. The largest single [std] lever in the product, and there is no public source for it and no observed range. 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 0.830575, then wins the race between relapse and exit with probability 0.393544, giving 0.326868 per cycle and an expected 1.485593 diagnosis payments per diagnosed life.

With repeat_conditioned the hazard is multiplied by treat_prob, the conditional probability of being in treatment on the [std] basis.

void_prob()

The probability of a diagnosis inside the 90-day window; zero in the base run.

1 - (1 - i(0))^W = 0.000368681 at the anchor cell, 0.037% of policies. A diagnosis inside the window makes the contract void, not merely unpayable — 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 rather than in the lapse column. void_adjust is off in the base run and the omission is quantified here rather than waved at.

pols_if_init()

The exposure in force at t = 0: one policy, less any validity adjustment.

The acquisition expense and the initial commission are deliberately not scaled by it: they were incurred whether or not the contract turns out to have been void.

pols_healthy(t)

In force at the start of month t and never diagnosed with an 悪性新生物.

(pols_healthy(t) - diag_first(t)) (1 - q(t)) (1 - w(t)). A life diagnosed in month t leaves this state before the decrement and takes the diagnosed mortality in its month of diagnosis [std]. An in-situ diagnosis does not move the life out: it is a second benefit tier, not a state change.

This is the population the premium rides on, and the population lapse applies to.

surv_canc(t)

sc(t): the survival factor of a diagnosed life over month t.

(1 - q_c(t)) (1 - w_c(t)), and in the base run w_c = 0, so it is pure mortality: a diagnosed policy leaves the book only by death.

unlock(t)

The trigger cohort whose two-year cycle expires at the start of month t.

trig(t - C) carried forward on diagnosed decrements alone. The cycle is a delay, not a rate, and the delay is implemented on the trigger history: a life triggered in month s enters locked, survives C months of diagnosed decrements and arrives in open in month s + C. Zero before t = C, and in fact zero before t = C + W because nothing can trigger inside the waiting period.

pols_locked(t)

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

(pols_locked(t) + trig(t)) sc(t) - unlock(t+1). A life that has just been paid cannot be paid again for C months; this is where it waits.

pols_open(t)

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

(pols_open(t) - diag_rep(t)) sc(t) + unlock(t+1). Eligible, not in payment: a fresh 再発 / 転移 / 新生 is what converts eligibility into a payment, at the relapse hazard, without limit and with no termination on payment.

pols_cancer(t)

The diagnosed in-force population, pols_locked(t) + pols_open(t).

The weight on all five care benefits. 0.11% of the in-force after twelve months at the anchor cell, and drawing ¥16,035 a month per life while it lasts.

pols_if(t)

The total in force at the start of month t, healthy plus diagnosed.

The weight on the maintenance expense — a waived policy is still serviced — but not on the premium, which rides on pols_healthy() alone.

pols_if_at(t, timing)

The in-force count at a named point inside month t.

The library-wide timing vocabulary, over the total book:

"BEF_DECR"

the start-of-month count, pols_if() — the weight on the result_cf() row of the same t.

"BEF_LAPSE"

after mortality and before lapse, summed over the two states, each decremented on its own basis: the never-diagnosed survivors of mort_rate_mth() plus the diagnosed survivors of mort_rate_canc_mth(). A single blended rate applied to pols_if() does not reproduce it.

"AFT_DECR"

after both decrements, which is pols_if() of t + 1.

What the vocabulary cannot show on this model is the movement that defines the product. The three timings are decrement timings, and the first diagnosis is not a decrement: diag_first() moves a life from pols_healthy() to pols_cancer() before the decrement, changing which benefits and which premium the life carries while leaving pols_if untouched at every one of the three points. Read pols_healthy(), pols_cancer() and diag_first() — all three published as columns of result_cf() and result_pols() — for the state movement; pols_if_at answers only how many lives are left, never which state they are in.

diag_first(t)

First 悪性新生物 diagnoses in month t: pols_healthy(t) i(t) cover(t).

The event that starts every benefit stream and simultaneously stops the premium, which is what makes premium and claims anti-correlated by construction on this product.

diag_rep(t)

Repeat diagnosis triggers in month t: pols_open(t) r cover(t).

A fresh 再発, 転移 or new primary on a life whose two-year cycle has expired. There is no lifetime cap on the count.

trig(t)

All diagnosis payment triggers in month t, first and repeat.

The quantity the two-year clock restarts from, which is why unlock() reads the trigger history rather than the first-diagnosis history.

insitu_avail(t)

Z(t): the probability the once-only 上皮内新生物 benefit is still unused.

Z(t+1) = Z(t) (1 - iz(t) cover(t)), from Z(0) = 1. A separate ledger rather than a flag on the diagnosis benefit, because the tier has its own cap, does not start the two-year cycle and does not trigger the waiver.

insitu_used(t)

The once-only 上皮内新生物 tier consumed per never-diagnosed policy before month t.

Accumulated straight off the published claim line, insitu_ev(s) / pols_healthy(s), with no reference to the insitu_avail() recursion. It exists so that check_insitu_ledger() can assert that the benefit paid and the availability remaining still sum to one.

insitu_ev(t)

上皮内新生物 diagnoses in month t: pols_healthy(t) Z(t) iz(t) cover(t).

Attaches to the never-diagnosed alone, because the tier is not payable once a full-rate benefit has been paid. It generates the reduced lump sum and the surgery benefit and nothing continuing [std]: 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 — and the direction of the error is stated: it understates the in-situ tier.

pols_death(t)

Deaths at the end of month t, from both states.

Mortality is a pure liability-releasing decrement here: the composite carries no death benefit, so there is no claims_death anywhere in the model. A life diagnosed in month t is already in the diagnosed state for this purpose.

pols_lapse(t)

Lapses at the end of month t, taken from the survivors of mortality.

Zero out of the diagnosed state in the base run. A lapse pays nothing — there is no surrender value at any duration under 終身払 — so this moves pols_if() and nothing else, and claims(t, "LAPSE") is identically zero.

hosp_stay_days(t)

L: the mean cancer hospitalisation in days.

14.4 days for 悪性新生物 discharges against 28.4 for all conditions, all ages, from 患者調査. With hosp_age_gradient on, the sourced four-band gradient — 10.7 at 35-64, 15.5 at 65+, 17.6 at 75+ — is read instead; the base run takes the all-ages figure [std] because the gradient is published on four broad bands and the incidence on twenty-one narrow ones.

hosp_rate_mth(t)

h: monthly cancer admissions per diagnosed life, hosp_rate / 12 [std].

The annual 0.25 is derived from two sourced counts on a trick that needs no population figure, because the population cancels: 2,689,653 cancer admissions a year — 106,100 inpatients times 365 over a 14.4-day mean stay — against 993,469 new diagnoses a year gives 2.707020 admissions per diagnosed person over a cancer lifetime, and spreading that over the 10.815-year mean diagnosed-state duration gives 0.250293. At 14.4 days each it is 38.98 inpatient days per diagnosed person, the single most useful number for sanity-checking an implementation.

The constant hazard makes the inpatient benefit proportional to survival, which is the product’s actual economics under an unlimited-day design; it does not front-load admissions onto the diagnosis month, which real cancer treatment does.

paid_months(t)

The qualifying treatment months paid in month t, min(p_tr, K - M(t)).

An indicator per month, not a count and not a duration. treat_prob = 0.10 [std] — 1.2 qualifying months per diagnosed life-year — has no public source and no observed range; the only calibration anchor is the cap itself, against which a life diagnosed at the anchor age accumulates an expected 12.98 months.

treat_months(t)

M(t): the treatment-month ledger, per diagnosed life, against the cap K.

M(t+1) = (M(t) + paid_months(t)) pols_cancer(t) / (pols_cancer(t) + diag_first(t)) — a cohort average diluted by new entrants, and only by first diagnoses, because a repeat trigger is an already-diagnosed life whose ledger continues. Zero while pols_cancer is zero.

The direction of the approximation is stated rather than discovered: E[min(sum, K)] != min(E[sum], K), so a deterministic average understates the cap’s bite. Here that matters more than on the medical chassis, because the 60-month cap is reached by a real minority rather than never. M(12) = 0.4002 at the anchor cell — small, and not therefore deletable.

adv_freq_mth()

f_a: the monthly 先進医療 療養 frequency per diagnosed life, adv_freq / 12 [std].

0.012 療養 per diagnosed life-year, with no observed range. The medical chassis carries the sourced 先進医療 cost anchors; this product’s own source set does not, so neither the frequency nor the severity can be tagged here.

adv_pay(t)

pay(t): the 技術料 reimbursable per 療養 in month t, min(S_a, LV - V(t)).

adv_sev = ¥600,000 [std], 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. The draw falls to zero when the ¥20,000,000 lifetime cap is reached, which is how the rider’s termination on the cap is implemented. Zero without the rider.

adv_paid(t)

V(t): the 先進医療 技術料 ledger, per diagnosed life, against the ¥20,000,000 cap.

Diluted by new entrants on the same cohort-average basis as treat_months(), and accumulating the 技術料 only — the 10% cash top-up is a benefit, not a draw against the cap. V(12) = ¥2,401.31 at the anchor cell.

pols_payer(t)

The in-force policies actually paying premium at the start of month t.

pols_healthy() on the composite, because the waiver fires on the first invasive diagnosis; pols_if() on the disability-trigger and no-waiver designs, where a cancer diagnosis does not stop the premium. Weighting the premium by pols_if on the composite overstates income by exactly the waived population.

premium_factor(t)

The repricing factor on the 10年更新 定期 chassis flag [std]; 1 in the base run.

The renewal recomputes the premium at then-current rates, which would ordinarily close the Solvency contract boundary at each renewal. jplib projects the flag to final expiry at a flat rate and records the tension rather than resolving it; set renew_reprice_rate above zero to step the premium at each renewal instead.

prem_payable(t)

Whether a premium falls due in month t: 1 during the premium-paying period, else 0.

終身払 pays for life. 65歳払済 stops at the 年単位の契約応当日 on which the insured attains 65, after which the cover continues unpaid — and so does the maintenance expense, which is what makes expense inflation a first-order lever on a short-pay design.

premiums(t)

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

P x pols_payer(t). On the composite that is P x pols_healthy(t): the waiver fires on the first invasive diagnosis, so the diagnosed pay nothing. The premium is still charged throughout the 90-day waiting period — five of the six carriers that state it charge from inception, and the one that does not says explicitly that its three free months are not a discount.

claims(t, kind=None)

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

"DIAG"

the がん診断一時金, DB x trig(t) — first diagnoses and repeats alike, with no lifetime cap and no termination on payment.

"INSITU"

the 上皮内新生物 tier, u x DB x insitu_ev(t): a second benefit at a second rate on its own once-only cap, not a discount on the first.

"HOSP"

the がん入院給付金, D x L x h x pols_cancer(t), with no per-hospitalization and no 通算 day limit.

"SURGERY"

the がん手術給付金, m_s x A times two limbs: surgeries on the diagnosed state at s_h per admission, and s_z surgeries recognised in the month of an in-situ diagnosis, since in-situ disease is by definition managed by local excision and the composite pays the benefit in full.

"TREAT"

the がん治療給付金, B_tr x paid_months(t) x pols_cancer(t) — JPY per month times months, with no day count anywhere in it.

"OUTPATIENT"

the がん通院給付金, A x o x pols_cancer(t). outp_days = 1.10 [std] per diagnosed life-year derives from 186,400 cancer outpatients on the survey day at 250 [std] operating days a year — 46.91 visits per diagnosed person — of which a 25% [std] share is treatment-linked and so qualifying. Both the 250 and the 25% are unsourced and between them they are a factor-of-four uncertainty.

"ADVANCED"

the 先進医療給付金, f_a (pay + min(10% pay, 500,000)) x pols_cancer(t).

"DISCHARGE"

the がん退院一時金, zero unless the rider is attached; a [std] construction, since the technical notes carry the flag but not the formula. See the Space docstring.

"LAPSE"

zero, always. There is no surrender value at any duration under 終身払; the kind exists so that the zero is stated rather than left to inference.

At the anchor cell’s parameters the five care benefits are fixed yen amounts 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 in total.

inflation_factor(t)

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

1.0% p.a. flat, stepping at each 年単位の契約応当日 rather than gliding monthly.

maint_expenses(t)

e(t): the maintenance expense at the start of month t [std].

¥250 per policy per month inflating at 1% p.a., on pols_if() — a waived policy is still serviced, so the expense runs on the diagnosed population with no premium against it. ¥250 against a ¥3,000 premium is 8.3% of premium, the premium is fixed for life and the expense is not, which is why the notes rate expense inflation a first-order lever despite its size.

claim_expenses(t)

The claim handling expense at the end of month t [std].

¥5,000 per diagnosis trigger — invasive or in-situ — and ¥3,000 per cancer admission. A cells of its own, deducted explicitly in net_cf() and published as its own claim_expenses column of result_cf(); it is not inside expenses(). Keeping it separate is what lets a reader see the policy-servicing cost and the claim-handling cost move independently, which on this product they do: the first rides on pols_if() and the second on the diagnosis and admission counts.

expenses(t)

Acquisition and maintenance expense in month t [std]; not claim handling.

¥20,000 per policy at t = 0, then the inflating maintenance expense. The claim handling expense is claim_expenses(), a separate cells with a column of its own — the library-wide split, so that expenses means the same thing in every model. No Japanese cancer expense scale is public; the levels are carried from the medical chassis and scaled to this product’s premium.

technical-notes.md’s month-by-month traces print the two in one arithmetic line — 250 x pols_if + 5,000 x diagnoses + 3,000 x admissions — because the notes narrate the month’s expense as a single sum. The worked-example table and the policy-year-1 aggregate carry the two as separate rows, matching the two columns published here; the notes’ combined figure is their sum.

commissions(t)

Commission outgo in month t [std].

1.5 times the annualized premium at t = 0 — ¥54,000 on the anchor cell — then 3.0% of premium income from policy year 2. No Japanese commission scale is public either. With the acquisition expense this is ¥74,000 of cost at outset against a ¥3,000 monthly premium: the product’s cost is almost entirely in front of it.

net_cf(t)

The net cash flow of month t, income positive.

Premiums less every benefit line, less expenses() (acquisition and maintenance), less claim_expenses() deducted explicitly, less commission. The notes’ own sign, which is also the library-wide convention, so there is no outgo-positive liability_cf companion to publish.

Note the asymmetry that defines this product’s cash-flow signature: premiums are weighted by pols_healthy() and claims by pols_cancer(), and the two are disjoint. Every error in incidence therefore hits both sides of the cash flow at once, roughly doubling its effect here.

check_pols_roll_fwd_resid(t)

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

pols_if(t) - pols_if(t+1) - deaths - lapses. There is no maturity term and no benefit-driven termination to add: the contract does not end and cannot exhaust, so a life leaves only by dying or lapsing. A first diagnosis cancels out of this identity because it moves a life between states rather than out of the book.

check_pols_roll_fwd()

True when the in-force roll-forward closes in every projected month.

The library-wide form of a roll-forward check: no argument, one bool over all t, so one test can call it across every model. check_pols_roll_fwd_resid() gives the signed residual of the month that failed.

check_cancer_roll_fwd_resid(t)

The diagnosed-state roll-forward residual in month t; zero everywhere.

pols_cancer(t+1) - (pols_cancer(t) + diag_first(t)) sc(t). The locked and open recursions each carry an unlock term of opposite sign, so their sum must collapse to this one line; a sign slip or an off-by-one in the delay shows up here and nowhere else in the in-force figures.

check_cancer_roll_fwd()

True when the diagnosed-state roll-forward closes in every projected month.

check_cycle_ledger_resid(t)

The two-year cycle ledger residual in month t; zero everywhere.

pols_locked() less an independent rebuild of the same figure — the triggers of the previous C - 1 months, each carried forward on diagnosed decrements — summed straight off the trigger vector with no reference to the unlock() recursion. A cycle implemented as a rate rather than as a delay, or one released a month early or late, shows up here.

check_cycle_ledger()

True when the two-year cycle ledger closes in every projected month.

check_insitu_ledger_resid(t)

The once-only 上皮内新生物 ledger residual in month t; zero everywhere.

insitu_avail(t) + insitu_used(t) - 1. insitu_used() is accumulated off the published claim line rather than off the ledger recursion, so the identity fails if the benefit is paid at a rate the ledger is not decremented by — which is what implementing the tier as a share of the main diagnosis benefit would do.

check_insitu_ledger()

True when the once-only 上皮内新生物 ledger closes in every month it is observable in.

The identity is read off the claim line, so it says nothing once the never-diagnosed population is exhausted: at the terminal age the best-estimate mortality reaches exactly 1, pols_healthy becomes zero and no in-situ benefit is paid, while insitu_avail() — a probability conditional on being never diagnosed and in force — keeps running against nobody. Those months carry no information and are excluded rather than papered over.

check_treat_cap_resid(t)

The treatment-month ledger’s excursion outside [0, K] in month t; zero everywhere.

Positive when the month’s draw would carry the ledger past the 60-month cap, negative if the ledger ever went below zero. This is the identity the cap exists to enforce, and it is the one a per-block rather than per-life ledger would break by deferring the cap forever.

check_treat_cap()

True when the treatment-month ledger stays inside its cap in every month.

check_adv_cap_resid(t)

The 先進医療 ledger’s excursion outside [0, LV] in month t; zero everywhere.

The rider terminates when the ¥20,000,000 lifetime cap is reached, so the ledger plus the month’s draw must never pass it.

check_adv_cap()

True when the 先進医療 ledger stays inside its cap in every month.

check_net_cf_resid(t)

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

Rebuilds net_cf from the columns of result_cf() rather than from net_cf(), so a column wired to the wrong cells, a benefit line dropped from the table or a double-counted claim expense shows up as a non-zero residual in the very table a reader is looking at.

The benefit side is every column whose name begins claims_, taken as a group rather than enumerated: result_cf() publishes the nine splits and no bare ``claims`` subtotal beside them, so the columns of the table sum to net_cf without a reader having to know which of them to skip. A benefit line added to the table and not to net_cf() is caught by the same sweep.

check_net_cf()

True when the published cash-flow statement adds up in every projected month.

result_cf()

Result table of cash flows, indexed by policy month t.

pols_if is the start-of-month count and the weight on the maintenance expense of the same row — but not on premiums, which is carried by pols_healthy, nor on the seven benefit lines, five of which are carried by pols_cancer. Publishing the three counts side by side is what makes that asymmetry visible in the table itself.

expenses is acquisition plus maintenance and claim_expenses is the claim handling cost, in two columns rather than one: the library-wide split, and on this product the two move on different weights.

net_cf carries the notes’ own income-positive sign. claims_lapse is a column of zeros by product design — there is no surrender value — and is published rather than dropped; claims_discharge is zero unless the がん退院一時金 rider is attached. There is no claims_death column at all, because the composite has no death benefit.

The nine benefit lines are published as splits and no bare ``claims`` subtotal is published beside them. The table’s columns therefore add to net_cf as they stand: premiums less every claims_* column, less expenses, claim_expenses and commissions. A subtotal column sitting among its own components would break that, since a reader summing the row would double the whole benefit side. The claims() cells still returns the total when its kind argument is omitted; it is the column that is not published. check_net_cf() asserts the identity off this table in every projected month.

result_pols()

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