The Projection Space#

The by-policy projection of the Term_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 is the 0-based projection index and its unit is the policy month: t = 0 is the first projected month and t = proj_len() - 1 the last, so proj_len() is the number of projected months and the frame is range(proj_len()). The contractual policy year is the 1-based label policy_year(t) = 1 + t // 12, derived and never indexed by, and duration(t) = t // 12 is the count of completed policy years that every contractual schedule in the product is quoted against. There is nothing after the last month — no 満期保険金 (maturity benefit), no 解約返戻金 (kaiyaku-henreikin, surrender value), no run-off and no tail state of any kind [S1][S8][S10][S14].

Where the horizon ends is a product question rather than a convention. A 歳満了 (sai manryō) contract ends at its stated age and never renews [S1], so proj_len() = 12 policy_term(). A 年満了 (nen manryō) 更新型 contract renews automatically at the end of every 保険期間 until it reaches the renewal ceiling of attained age 80 [S1][S2][S8], so proj_len() = 12 (renew_ceiling() - age_at_entry()) and a ten-year term issued at 30 is projected for 600 months across five priced terms. contract_boundary = current_term truncates instead at the end of the term in force at the valuation date.

The monthly grid, and what it changes

Everything the composite guarantees is still quoted in years — the 保険期間, the renewal ceiling, the lapse curve, the mortality table — so the monthly step does not make the contract finer; it makes the projection of it finer, and four things move as a result.

Rates convert, one-off proportions do not. The mortality and lapse decrements are annual rates and are taken to the month on the effective convention r_m = 1 - (1 - r)^(1/12), which is mort_rate_mth() and lapse_rate_mth(); twelve of them compound back to the annual rate exactly. The renewal decline is not a rate per unit time — it is the proportion of survivors who walk away when a 保険期間 ends — so decline_rate() is applied unconverted in the single month the term expires. Converting it would spread one decision over twelve months; annualizing the other two would apply a year of decrement to a month of exposure.

The premium is now paid when the contract says it is. premium_mode was inert on the annual grid, which annualized every mode into one start-of-year payment; here prem_mode_months() and prem_due_pp() pay 月払 monthly, 半年払 every sixth month and 年払 every twelfth. The rate cards this product is priced off are quoted monthly [S2], so the monthly grid is also the grid the premium is stated on.

One [std] approximation is retired rather than restated. The annual model collected a whole year of premium in advance from lives that might exit in month two, and offset that against claims booked at the end of the year; the notes declared the pair matched and warned against correcting either alone. Neither approximation survives here, so neither offset is needed, and the undiscounted totals move accordingly — the anchor cell collects ¥457,507.04 of premium against the annual grid’s ¥470,348.54, because it stops collecting from lives that have already gone.

The strain is where it actually falls. Acquisition expense and initial commission are one month’s outgo against one month’s premium, so t = 0 is a far deeper hole than the annual grid’s first row and every later month is shallower. The total is the same money; the shape is the one a cash flow statement is for.

What does not move is the survivorship at the anniversaries, and that is worth knowing because it is the check that the conversion was done right. The effective convention makes (1 - q_m)^12 = (1 - q) and (1 - w_m)^12 = (1 - w) exactly, and the renewal decline falls in the month a policy year ends either way, so pols_if(12 j) here equals the annual model’s pols_if(j) to floating-point: l(120) = 0.466683 and l(600) = 0.026042, the same two numbers the annual grid published. Every difference in the cash flows is therefore a timing difference and never a difference in the decrement basis — which is what makes the two runs comparable at all.

Input data

Inputs are external files: plain CSVs living in the model folder’s parent directory, products/term_life/, 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 Term_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
lapse_table_file	data.lapse_table()	lapse_table.csv
prem_rate_file	data.prem_rate_table()	prem_rate_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 rates, *_pp for per-policy amounts, claims(t, kind) with an uppercase kind string, pols_if_at(t, timing) for the within-month in-force reads, and the annual / *_mth pair for a rate that is quoted per annum and applied per month. The technical notes use compact actuarial symbols instead. The mapping is:

Notes symbol	Cells	Meaning
(row label)	model_point()	The selected model point row
t	(the index of result_cf)	Policy month, 0-based
floor(t/12)	duration(t)	Completed policy years
y(t) = 1 + floor(t/12)	policy_year(t)	Contractual policy year
x	age_at_entry()	契約年齢, 満年齢
x + floor(t/12)	age(t)	Attained age in month t
(none)	sex()	Rating factor, M or F
(none)	term_type()	nen (renewable) or sai
n	policy_term()	保険期間, in years
12n	term_months()	保険期間, in months
w_r	renew_ceiling()	Attained age renewal stops
N	horizon_ceiling()	Years from entry to w_r
t = 0..12N-1	proj_len()	Number of projected months
(none)	contract_boundary()	ceiling or current_term
k	term_index(t)	Term index, 1 in the first
x_k	term_start_age(k)	Attained age at term k start
m_k	term_len(k)	Length of term k, truncated
SA	sum_assured()	保険金額, level
f	policy_fee_m()	Flat monthly element, 248
r(sex, x, m)	prem_rate_m(t)	Rate per 5,000,000 of cover
qbar(x, m)	mort_table_mean(x, m)	Mean table rate over m years
P_m(k)	premium_mth_pp(t)	Monthly premium, whole yen
P_a(k)	prem_pp(t)	Annualized premium
(mode)	prem_mode_months()	1, 6 or 12
(none)	prem_due_pp(t)	Premium falling due in month t
(table)	mort_rate_at_age(x)	Table rate at an age
(table)	mort_rate_base(t)	Table rate in month t, annual
(margin removal)	mort_be_factor	Best-estimate factor, 0.80
lambda	sel_lapse_lambda	Selective-lapsation loading
l_ref	sel_lapse_ref	Selective-lapsation reference
(none)	sel_lapse_factor(t)	Mortality loading on stayers
q(t)	mort_rate(t)	Death and 高度障害, annual
q_m(t)	mort_rate_mth(t)	The same, per month
w(t)	lapse_rate(t)	Ordinary lapse rate, annual
w_m(t)	lapse_rate_mth(t)	The same, per month
d(t)	decline_rate(t)	Renewal decline, not a rate
d_0	decline_base	Flat decline rate, 15%
beta, d_max	decline_beta, decline_max	Decline elasticity module
l(t)	pols_if(t)	In force at start of month t
(within-month)	pols_if_at(t, timing)	BEF_DECR / BEF_LAPSE / …
D(t)	pols_death(t)	Expected claims in month t
(none)	pols_lapse(t)	Ordinary lapses
(none)	pols_decline(t)	Renewal declines
lap(t)	pols_lapse_pool(t)	Reinstatable population
rho	reinstate_rate	Reinstatement rate, annual
rho_m	reinstate_rate_mth()	The same, per month
W	reinstate_window	3 years [S1]
12W	reinstate_window_m()	36 months
(none)	pols_reinstate(t)	Reinstatements into l(t+1)
(none)	pols_lapse_expire(t)	Pool leavers, window expired
(none)	wop_waived_frac(t)	Fraction with premiums waived
inc_m, rec_m	wop_inc_rate_mth(), …	Waiver chain, per month
(none)	pols_payer(t)	Policies paying premium
A	ln_amount()	Accelerated amount
i_ln	ln_interest_rate	Six-month discount rate
a(t)	ln_share(t)	Acceleration take-up
(payout formula)	ln_payout_pp(t)	A - interest - premiums
P x l	premiums(t)	Premium income
SA x D(t)	claims(t, kind)	Benefit outgo by kind
ec	expense_claim	Claim expense per claim
ec x D(t)	claim_expenses(t)	Claim expense outgo
E0	expense_acq	Acquisition expense, 15,000
e_m(t)	expenses(t)	Acquisition + maintenance
c0	comm_init_pp()	Initial commission per policy
c_r	comm_renewal_rate	Renewal commission rate, 5%
(footnote 4)	comm_new_term(t)	Commission at a 更新
(none)	commissions(t)	Commission outgo
CF(t)	net_cf(t)	Net cash flow, income positive

Five names needed care.

The notes write q(t) for the decrement and qbar(x, m) for a mean of table rates used by the premium scale. Those are different quantities on different bases — one is best-estimate and one is not — so they get different names: mort_rate() is the decrement, and mort_table_mean() averages mort_rate_at_age(), which reads the table unadjusted. Feeding the best-estimate rate into the premium extension would move a premium scale by an assumption that has nothing to do with pricing.

P_m(k) and P_a(k) are indexed by the term in the notes and by the policy month here. premium_mth_pp() and prem_pp() take t and resolve the term through term_index(), which is what keeps every cash flow line indexed the same way. The premium is nonetheless level within a 保険期間, and check_prem_level() asserts it.

prem_pp is the annualized premium and is not the premium cash flow on this grid. prem_due_pp() is: it is what the payment mode makes fall in month t, and on a 年払 point it is zero in eleven months out of twelve. prem_pp survives because the repricing rule, the commission scale and the renewal ladder are all quoted per annum, and because a cells that meant “premium” in two senses would be worse than two cells.

d(t) is spelled decline_rate(), not any variant of lapse. It is a different event at a different time from a different population — see below — and the name is the first line of defence against the two being merged.

lap(t) is spelled pols_lapse_pool() because it is a stock, the lapsed lives still inside the three-year 復活 window, whereas pols_lapse() is the month’s flow into it.

更新 reprices; it does not re-issue

This is the structural difference from this repository’s UK term model and the notes’ second-listed pitfall. At a renewal boundary the premium is recomputed on attained age and on the scale then in force [S1][S4][S8][S12], and nothing else resets:

pols_if is continuous across the boundary. There is no reset to 1.
No acquisition expense and, in the base run, no commission is paid at a renewal (comm_new_term_rate is 0). A 更新 is not new business: no new 保険証券 is issued and no 告知 is taken [S1][S4].
The suicide and contestability clocks run from the original 責任開始日 and do not restart on 更新 [S1][S4][S7][S8]. Only 復活 restarts them [S1]. Neither clock is monetized in the base run, so neither is a cells; both are stated here because treating each renewed term as a fresh policy gets persistency, the strain pattern and both clocks wrong at once.

Truncation at the ceiling shortens the term, not the horizon: a renewal that would carry the policy past attained age 80 renews as an 80歳満了 term instead [S1][S2][S8], so an issue age of 35 has a final term of five years and the projection still ends exactly at 80. That is term_len(), and model point 4 exercises it. Three other market rules exist — shorten to expiry age 90, shorten or lengthen to a 指定年齢, auto-convert to another product [S4][S7][S12] — and importing one changes the horizon.

Renewal decline is not lapse

decline_rate() is non-zero only in a boundary month, and the exits it produces are taken after mortality and after ordinary lapse — the notes’ processing order, steps 3, 4 and 5. On the anchor cell that month is t = 119, the last month of the first 保険期間, and there the decline removes 15% of the survivors against a month of ordinary lapse of about 0.43% and a month of mortality of about 0.007%: better than 97% of that month’s exits. The annual grid could only say 74%, because it compared one renewal decision with a whole year of lapse. Folding the decline into lapse_rate() makes the boundary invisible and mis-times most of the cohort’s departure.

That is also the clearest thing the finer grid buys on this product. A renewal is an event at a date, and on the monthly grid it is projected as one.

Two behaviours roll into the one rate, and a production model should separate them: the policyholder who gives notice to decline, and the policyholder whose first renewed premium goes unpaid through grace, in which case the renewal is treated as never having happened and the contract terminates at the original expiry [S1][S7]. Only the first is a decision. Both leave at the boundary, which is why one rate can carry them — and why neither may appear in force at t + 1 collecting the renewed premium. The monthly grid makes the second of the two representable for the first time — grace is about a month long [S1][S8], so a model that wanted to separate them now has a period short enough to put the unpaid-premium exit in — but separating them would need a take-up assumption the sources do not give, so the composite keeps one rate.

One decrement, one benefit

生保標準生命表2018（死亡保険用）**includes 高度障害** (kōdo shōgai, severe disability) inside its death rate [REG-R20], and the contract pays one sum assured and terminates on whichever of the two events comes first [S1][S8]. mort_rate() is therefore the combined death-and-高度障害 decrement, and there is no disability incidence anywhere in this model. Adding one on top of the table double-counts the benefit — the notes’ first-listed pitfall.

The same reasoning governs the リビング・ニーズ特約 module below: an acceleration is a re-timing and re-pricing of the death benefit, not a second claim, so ln_share() splits the existing decrement rather than adding to it.

Lapse pays nothing, and there is no 自動振替貸付

There is no 解約返戻金 at any duration on this composite [S1][S4][S6][S8][S9][S10][S13][S14], so an ordinary lapse is a pure decrement: it moves pols_if() and pays nothing. claims(t, "LAPSE") exists and returns zero, and result_cf() carries the zero column, because the notes list a non-zero lapse row as a pitfall imported from models with cash surrender values — and because one carrier in eight does write this design with a surrender value [S12], so the zero is asserted from the composite’s sources rather than assumed from the product class.

There is no 自動振替貸付 (jidō furikae kashitsuke, automatic premium loan), stated in terms by one carrier [S7], and no collateral for a 契約者貸付 either — the second an inference from the missing surrender value rather than a citation, since that carrier points its policyholders at the 契約貸付制度 instead [S7] and the document appearing to rule the policy loan out could not be extracted [S11]. Importing the APL mechanic that WholeLife_JP_S carries would create a no-lapse cushion this contract does not have. Grace, then 失効, then 復活-or-not is the whole persistency machinery here.

The premium chassis, and where it stops being sourced

Japanese carriers publish rate cards, so the structure decomposes exactly [S2]:

P_m(k) = f + r(sex, x_k, m_k) * SA / 5,000,000
x_k    = x + (k - 1) * n
m_k    = min(n, w_r - x_k)
P_a(k) = 12 * P_m(k)

with f = 248 per month and P_m rounded to the whole yen, which is the granularity rate cards are published at [S2][S9][S10]. On this grid P_m is the cash flow and P_a the pricing quantity; the payment mode decides how many months’ worth of P_m fall in a given month, through prem_due_pp(). Four cells are sourced — male ages 30, 40 and 50 and female age 30, all at a ten-year term. Ages 60 and 70 are published by no carrier, and the anchor cell reaches both, so prem_rate_m() extends the scale off the is_anchor row of the matching sex [std]:

r(sex, x, m) = r_anchor * mort_table_mean(x, m) / mort_table_mean(x_a, m_a)

The extension back-casts to ¥958.9 at age 30 against the published ¥974 (-1.5%) and to ¥1,806.4 at age 40 against ¥1,823 (-0.9%), and gives ¥8,976 at 60 and ¥23,881 at 70. Published cells are always used where they exist; the extension fills the gaps. That the back-cast is close is reassuring about the form and says nothing about the level an insurer will charge in 2056 — the notes rate it the third-largest lever on this cell.

The ¥248 is a premium component, not an expense recovery [S2]. It enters the model only through premium_mth_pp(); crediting it against maintenance expense counts it twice.

Modules that are off in the base run

Eight of the notes’ optional constructions are implemented and switched off, so that the base run reproduces the worked example while the machinery stays visible and testable. Three of them are model point columns, five are References:

リビング・ニーズ特約 (living_needs), a discounted acceleration of the death benefit. Off on the anchor cell; on for model points 6 and 9.
保険料の払込の免除 (wop), the premium waiver on an accident-caused 別表4 state. Off on the anchor cell; on for model point 7. 別表4 is a materially lower bar than the 別表3 test for 高度障害 — loss of one eye, deafness in both ears, loss of one limb at the wrist or ankle [S1] — so the waiver incidence is not the 高度障害 incidence and wop_waived_frac() does not reuse mort_rate().
復活 (reinstatement), the lapsed-but-reinstatable population and its three-year window [S1]. Off on the anchor cell; on for model point 8.
Contract boundary (contract_boundary), current_term truncating at the end of the 保険期間 in force at the valuation date. ceiling on the anchor cell; current_term on model point 5. The two differ by more than a rounding — +¥47,254.64 against -¥16,071.24 on the same cell — and the ESR standard-model treatment of a no-underwriting auto-renewal that would settle which is right is [unverified] here [REG-R16], so the model does not rule.
Selective lapsation, q_eff = q (1 + lambda max(0, 1 - l(t)/l_ref)), with sel_lapse_lambda = 0. Stronger here than on a UK term policy: renewal takes no 告知 [S1][S4][S8][S12], so a life that has become uninsurable elsewhere renews while a healthy life re-shops, and the decision recurs four times on the anchor cell.
Renewal-decline elasticity, d = min(d_max, d_0 (P_a(k+1)/P_a(k))^beta), with decline_beta = 0 giving the flat 15%. The premium jump the elasticity would respond to accelerates: 1.87, then 2.16, 2.28 and 2.66.
Age-basis shift, q_x -> sqrt(q_x q_(x+1)), with mort_age_shift = False. 契約年齢 is 満年齢 (man-nenrei, age last birthday) [S1] while 標準生命表2018 is built for 保険年齢 (hoken-nenrei, age nearest birthday) [REG-R20], so reading the table at 満年齢 reads it half a year early and understates mortality. The base run accepts and states that bias; the shift module must move q up, not down — about 0.7% at age 30 and 4.2% at age 40.
Commission at 更新, comm_new_term_rate = 0. Set it to reproduce a scale paying first-year rates on each renewed term, which would change the sign of the cash flow at t = 120, 240, 360 and 480. No document in the source set discloses a commission scale at all, so the zero is a choice and not a fact.

Sign convention and premium timing

The notes’ CF(t) is already income positive — they write + = inflow — 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.

Premiums fall at the start of the month on the payment mode the contract carries, and claims at the end of the month in which they arise. There is no half-year correction to make and none to double-count: the annual grid needed one because it collected a whole year of premium from lives that could exit in month two and booked their claims twelve months late, and this grid does neither. The residual timing convention is within a single month and is worth about a fortnight of interest on one month’s cash flow, which this model does not discount in any case.

What is not modelled, and why

減額 (a reduction in sum assured) changes SA and P_a together, which is a model point re-parameterization rather than a decrement [std scope] [S1][S8]. クーリング・オフ is out of scope: the projection begins with cover in force and the eight-day statutory population already out [REG-R36][S1]. The 復活 arrears, payable at 年6% compound [S1], are not monetized: they settle premiums for years in which this projection collected none, so recognizing them would need a missed-premium ledger the notes do not specify [std scope]. And a partial acceleration under リビング・ニーズ特約 leaves a reduced contract in force at a reduced premium [S1][S7] — a second transition, not one benefit with two amounts — so ln_amount() raises rather than approximating it. It cannot arise inside the composite’s ¥1,000,000-¥30,000,000 envelope, where the ¥30,000,000 per-insured cap is exactly reached at the ceiling and never reduces a single-contract payment: ln_cap_binds() tests that with a strict inequality.

Cells Descriptions#

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

sex()[source]#: The sex (M / F) of the insured, a rating factor of the premium scale [S2].

age_at_entry()[source]#

x: the 契約年齢 (issue age), 満年齢 with fractions discarded [S1].

Age last birthday, not age nearest birthday. 生保標準生命表2018（死亡保険用）is built for a 保険年齢 basis [REG-R20], so reading it here reads it half a year early and understates mortality; mort_age_shift is the optional correction and the Space docstring states the direction. The composite’s envelope is 20-65 [S1][S2].

term_type()[source]#

nen for a 年満了更新型 contract, sai for a 歳満了 one [S1][S4][S7].

The single most consequential model point attribute. A 年満了 contract renews automatically at attained-age rates to the ceiling; a 歳満了 contract has one term, one premium and no repricing [S1], and applying the renewal machinery to it invents cover the contract does not have.

policy_term()[source]#

n: the 保険期間 in years — the priced term, not the projection horizon.

Read from term_y on a 年満了 point and implied by expiry_age on a 歳満了 one [S1][S4]. On a 更新型 contract the horizon is horizon_ceiling(), which is longer, because the contract renews.

renew_ceiling()[source]#

w_r: the attained age at which renewal stops, 80 on the composite [S1][S2][S8].

Observed ceilings run 75 to 99 and 80 is the mode; behaviour at the ceiling varies more than the ceiling does, and the composite truncates into an 80歳満了 term rather than shortening to another expiry age or converting to another product [S4][S7][S12].

sum_assured()[source]#

SA: the 保険金額, level for the whole term and unchanged through 更新.

Paid on death or on a 別表3 高度障害 state, whichever becomes payable first; either terminates the contract and the other is then not paid [S1][S4][S8][S9][S12]. The composite’s envelope is ¥1,000,000-¥30,000,000 in ¥1,000,000 units [S2][S9][S13].

premium_mode()[source]#

Monthly, semiannual or annual premium payment [S1].

Live on this grid. The annual-step predecessor annualized every mode into one start-of-year payment and carried this column inert; the monthly grid pays the premium when the contract says it falls, through prem_mode_months() and prem_due_pp(). Model points 3 and 9 are 年払 and model point 7 半年払, so the difference is exercised by the shipped table rather than merely available.

contract_boundary()[source]#

ceiling or current_term: how far the liability is projected.

A Japanese 年満了 contract guarantees its premium only within the current 保険期間; at each 更新 the insurer recomputes it on attained age and the scale then in force [S1][S4][S8][S12]. That is a unilateral repricing right exercisable every ten years — but a scale-level right, not an individual one, because renewal takes no 告知 and no fresh underwriting, so the insurer cannot reprice a life for its own deterioration. The ESR coefficients that would settle where the boundary falls were not retrieved [REG-R16], so the model does not rule: it projects to the ceiling in the base run [std] and carries the truncation as a switch. Naming the convention is part of reporting the number.

living_needs()[source]#: Whether the リビング・ニーズ特約 acceleration module is on; false in the base run.

wop()[source]#: Whether the 保険料の払込の免除 module is on; false in the base run [S1][S8].

reinstatement()[source]#

Whether the 復活 module is on; false in the base run [S1].

Off by default because reinstate_rate = 0.10 is an arbitrary placeholder with a material persistency effect: no carrier in the source set publishes a reinstatement rate, no industry statistic in the set gives one, and no observed range can be quoted. A round tenth was chosen for the same reason as ln_take_up — so that no reader reads it as an estimate — and the only defence of it is that the module is off in the base run, leaving the worked example and every published figure independent of it. What is published, and is therefore not [std], is the window — three years, against arrears at 年6% compound [S1], on evidence of health [S8] — which is why reinstate_window is sourced while the rate beside it is not.

horizon_ceiling()[source]#

N: policy years from entry to the renewal ceiling.

renew_ceiling() - age_at_entry() on a 年満了 point, because the contract renews until it gets there [S1][S2][S8]; the term itself on a 歳満了 point, which never renews [S1].

proj_len()[source]#

The number of projected policy months: 12 N, or the current term’s.

The frame is range(proj_len()), so t runs 0 .. proj_len() - 1 and len(result_cf()) == proj_len(). contract_boundary = current_term truncates at the end of the 保険期間 in force at the valuation date, which for a policy projected from issue is policy_term() years. On a 歳満了 point the two coincide.

Twelve rows to the policy year, so the anchor cell’s fifty-year horizon is 600 rows and its boundary months are t = 119, 239, 359, 479 — the last month of each 保険期間 — rather than the annual grid’s t = 9, 19, 29, 39.

duration(t)[source]#

The number of completed policy years at the start of policy month t, t // 12.

The bridge between the monthly projection index and every contractual schedule in the product, all of which are quoted in years: the 保険期間 n, the renewal ceiling, the policy_year column of lapse_table.csv and the attained age the mortality table is read at. Months t = 0 .. 11 are all duration 0, the first policy year.

policy_year(t)[source]#

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

The 1-based label beside the 0-based month index — t = 0 .. 11 is policy year 1 — and the key into lapse_table.csv, whose policy_year column is 1-based for the same reason. It is derived, never indexed by: every cells of this model is indexed by the 0-based month t.

age(t)[source]#

x + floor(t / 12): the attained age (満年齢) at the start of policy month t.

t is 0-based, so the 契約年齢 holds for the twelve months t = 0 .. 11 and the contractual policy year is policy_year(t). The table this feeds is graduated by 整数年齢, so the age steps once a policy anniversary and not once a month.

term_index(t)[source]#

k: the term index — 1 in the original 保険期間, 2 after the first 更新, and so on.

1 + floor(duration(t) / n) on a 年満了 point; always 1 on a 歳満了 one, which never renews [S1]. k is a contractual, 1-based label and does not shift with the projection index. The premium is a function of k and not of t, which is the state variable a Japanese term model needs and a UK one does not.

Going through duration() rather than through t is what keeps the term index a contractual quantity on the monthly grid: a 保険期間 is n years, so the index turns over at t = 12 n, not at t = n.

term_months()[source]#

12 n: the length of a full 保険期間 in policy months.

The renewal period on the projection grid. A 保険期間 ends in the month t where (t + 1) % term_months() == 0 — t = 119 on the anchor cell — and that is the only month decline_rate() can be non-zero in.

term_start_age(k)[source]#: x_k: the attained age at which term k starts, x + (k - 1) n.

term_len(k)[source]#

m_k: the length of term k in years, min(n, w_r - x_k).

Truncation at the ceiling shortens the term, not the horizon: a renewal that would carry the policy past attained age 80 renews as an 80歳満了 term instead [S1][S2][S8]. An issue age of 35 on a ten-year term therefore has a final term of five years and still ends exactly at 80. The truncated term is priced over its own shorter length, which is why this feeds prem_rate_m().

omega_age()[source]#

The highest attained age the shipped mortality table carries for this sex.

Used only to keep the optional age-basis shift from reading past the end of the table; no shipped model point comes near it.

mort_rate_at_age(x)[source]#

The table mortality rate at attained age x, unadjusted.

A [std] proxy for 生保標準生命表2018（死亡保険用）, anchored on the rates the technical notes quote and attribute [REG-R18][R4]; see Data. This is the valuation-table rate with its own margin still in it, and it includes 高度障害 [REG-R20]. It is read directly by the premium scale and only through mort_rate_base() by the decrement.

mort_table_mean(x, m)[source]#

qbar(x, m): the mean table rate over ages x .. x + m - 1.

The shape parameter of the [std] premium extension. Deliberately built on the table rate rather than on mort_rate(): a premium scale is not a best-estimate quantity, and feeding the best-estimate factor in would move a published rate card by an assumption that has nothing to do with pricing.

mort_rate_base(t)[source]#

The table rate at the attained age of policy month t, before the margin removal.

An annual rate, read at age(t) and therefore level across the twelve months of a policy year; mort_rate_mth() turns it into the monthly decrement.

Optionally shifted to sqrt(q_x q_(x+1)) [std] when mort_age_shift is set, the correction for reading a 保険年齢 table [REG-R20] at 満年齢 [S1]. The shift raises the rate — about 0.7% at age 30 and 4.2% at age 40 — because the unshifted read is half a year early and understates. Off in the base run. The monthly grid does not dispose of it: the age still steps once a policy anniversary, so the half-year bias is the same one the annual grid carries, and interpolating q across the year would be a different and undocumented adjustment rather than this one.

sel_lapse_factor(t)[source]#

The selective-lapsation loading on mortality in policy month t [std].

1 + lambda max(0, 1 - l(t)/l_ref). Lapsers and decliners are healthier than stayers, so a block that has shed a large proportion of its lives carries impaired mortality on the remainder. The mechanism is stronger here than on a UK term policy and one-directional: renewal takes no 告知 [S1][S4][S8][S12], so a life that has become uninsurable elsewhere renews while a healthy life re-shops — and the decision recurs at every boundary. Off in the base run (sel_lapse_lambda = 0), where it returns 1 in every month. sel_lapse_ref = 1.0 [std] is the cohort at issue, so the loading is driven by the proportion of the original block that has left.

mort_rate(t)[source]#

q(t): the annual best-estimate death-and-高度障害 rate in policy month t.

mort_be_factor times the table rate, then the selective-lapsation loading, capped at 1. This is the annual rate the table is stated on; mort_rate_mth() is the decrement actually applied to the month. The pair follows the library’s convention — mort_rate annual, mort_rate_mth monthly — so that a rate quoted in the notes can be compared with the cells that carries it without a conversion in between.

One decrement carrying one sum assured: 生保標準生命表2018（死亡保険用） includes 高度障害 inside its death rate [REG-R20] and the contract pays once and terminates on whichever event comes first [S1][S8], so projecting the table rate for death and adding a 高度障害 incidence on top double-counts the benefit.

mort_be_factor = 0.80 [std] is this model’s largest single lever and its least evidenced number. The table’s 作成概要 sizes its margin to hold the exceedance probability near 2σ, capped at 130% of the unadjusted rate [REG-R20], and removing a margin at its cap implies 1/1.3 = 0.769; against that the table already carries a forward improvement allowance and its base experience is 2008, 2009 and 2011. 0.80 is a round central choice between the two. No observed range can be given: no Japanese insurer publishes protection experience by duration.

mort_rate_mth(t)[source]#

q_m(t): the monthly death-and-高度障害 decrement, 1 - (1 - q(t))^(1/12) [std].

The effective convention, not a nominal q / 12: twelve months of it compound back to exactly the annual rate, which is what makes the monthly projection comparable with the annual one rather than merely finer. At the anchor cell’s attained age 30 it is about 4.534e-05 against an annual 0.000544, and a nominal q / 12 would be 4.533e-05 — the difference is small here and is not small at attained age 75, where the same choice moves the month’s claims by 2%.

This is the cells the roll-forward and the claim line use; mort_rate() above is the annual rate it is built from and is what the assumption tables and the notes quote.

lapse_rate(t)[source]#

w(t): the annual ordinary lapse rate of the policy year containing month t [std].

9 / 7 / 6 / 5.5 / 5 percent, from lapse_table.csv, which is keyed by the contractual, 1-based policy year and so is read at policy_year(); policy years beyond the table take its last row. The level is anchored to the LIAJ’s FY2024 whole-market 解約・失効率 of 5.6% of opening in-force sum insured [REG-R31] — the simple mean over the first ten years is 5.75% and the in-force-weighted mean 5.94%, both a little above it, which is the expected direction for an early-duration protection curve against a figure dominated by long-duration in-force. The shape is a convention with no Japanese published evidence behind it.

A lapse pays nothing: there is no 解約返戻金 at any duration [S1][S4][S8].

lapse_rate_mth(t)[source]#

w_m(t): the monthly ordinary lapse rate, 1 - (1 - w(t))^(1/12) [std].

The same effective convention as mort_rate_mth(), and it matters more here because the rates are two orders of magnitude larger: the anchor cell’s first policy year is 9% a year, which is 0.783% a month effective against 0.750% nominal, a 4.4% difference in the month’s exits. Spreading an annual lapse rate over twelve months by division would shed 9.0% of the cohort over months that compound to 9.4%.

decline_rate(t)[source]#

d(t): the renewal-decline rate — non-zero only in a boundary month [std].

A proportion of survivors leave at each 更新 rather than accept the repriced contract. This decrement has no analogue in this repository’s UK or U.S. term models and it is large: on the anchor cell the monthly premium moves from ¥974 to ¥1,823 at the first renewal, a factor of 1.87 [S2]. Against that, renewal is the default — it happens unless notice is given, and the notice period is two weeks [S1][S8], the shortest of the three observed and the design that maximizes renewal by inertia. No carrier publishes a take-up or decline rate, so decline_base = 15% at every boundary.

It is not annualized and never converted to a monthly rate. It is a one-off proportion of the survivors of a single month — the month the 保険期間 ends — and not a rate per unit time, so the 1 - (1 - r)^(1/12) treatment mort_rate_mth() and lapse_rate_mth() get would be a category error here. It is the one decrement in this model the monthly grid leaves exactly as the annual grid had it, and that is the gain the finer grid buys: on the annual grid the decline was mixed into a year that also carried twelve months of ordinary lapse, and here it stands alone in its month.

Non-zero where a 保険期間 ends, which on the 0-based monthly frame is (t + 1) mod 12n = 0 — t = 119, 239, 359, 479 on the anchor cell. Zero on a 歳満了 point, which never renews [S1], and zero in the final projected month t = proj_len() - 1, where the cover ends at the ceiling rather than renewing. The optional elasticity d = min(d_max, d_0 (P_a(k+1)/P_a(k))^beta) responds to the premium jump, which itself accelerates — 1.87, then 2.16, 2.28 and 2.66 across the anchor cell’s four renewals; decline_beta = 0 in the base run gives the flat rate. decline_max = 0.50 [std] caps it: at beta = 1 the largest jump reaches only 40%, so the cap binds at no boundary, while at beta = 2 it binds at every one.

policy_fee_m()[source]#

f: the flat monthly element inside the premium, ¥248 [S2].

A premium component, not an expense recovery. It enters the model only through premium_mth_pp(); crediting it against expenses() counts it twice. Read from the is_anchor row of the matching sex, which is where the decomposition of the published rate card is recorded.

prem_rate_m(t)[source]#

r(sex, x_k, m_k): the marginal monthly rate per ¥5,000,000 of cover in month t.

The published cell where one exists [S2] — male ages 30, 40 and 50 and female age 30, all at a ten-year term — and otherwise the [std] extension off the is_anchor row of the matching sex:

r(sex, x, m) = r_anchor * qbar(x, m) / qbar(x_a, m_a)

Ages 60 and 70 are published by no carrier and the anchor cell reaches both, so the extension is unavoidable rather than optional. It back-casts to ¥958.9 at age 30 against the published ¥974 (-1.5%) and to ¥1,806.4 at age 40 against ¥1,823 (-0.9%), which is reassuring about the form of the scale and says nothing about the level an insurer will charge decades out.

premium_mth_pp(t)[source]#

P_m: the monthly premium per policy in policy month t, in whole yen.

f + r(sex, x_k, m_k) SA / 5,000,000, rounded half up to the yen, which is the granularity published rate cards are quoted at [S2][S9][S10]. Level within the 保険期間 and recomputed at each 更新 on attained age [S1][S4][S8][S12]; it is not guaranteed beyond the current term, which is what makes contract_boundary a question rather than a detail.

On the anchor cell this reproduces the published ¥974 exactly: 248 + 2 x 363. It is the rate card’s own quantity, and on the monthly grid it is also the cash flow: the annual grid had to annualize it to get a row, and this one does not.

prem_mode_months()[source]#

The number of months between premium payments: 1, 6 or 12 [S1].

月払 pays every month, 半年払 every sixth and 年払 every twelfth, the first instalment of each falling at t = 0. The mode is live on this grid and was inert on the annual one, which annualized every mode into one start-of-year payment: the monthly grid is the first place in this model where a 年払 policy and a 月払 policy have different cash flows, and the difference is a timing difference of up to eleven months on every premium the contract collects.

What does not change with the mode is the amount per year. Mode discounts and 前納 (advance payment) discounts are insurer-set and unpublished [S1][S7][S9][S14], so a 年払 policy pays 12 P_m once rather than a discounted annual premium [std].

prem_due_pp(t)[source]#

The premium falling due per paying policy at the start of policy month t.

P_m every month on 月払; prem_mode_months() months’ premium at the start of each payment period and nothing in between on 半年払 and 年払, the first falling at t = 0. Zero outside the projection.

The payment clock runs from issue, not from the start of the current 保険期間, so a 年払 policy renewing at t = 120 pays its renewed premium in that same month because 120 % 12 == 0; that is true of every 保険期間 here because the terms are a whole number of years. Where a truncated final term is not — it cannot be on this composite, since the ceiling is reached in whole years — the clock would still be the issue clock.

prem_pp(t)[source]#

P_a: the annualized gross premium per policy in policy month t, 12 P_m.

Not a cash flow on this grid — prem_due_pp() is — but the pricing quantity the contract is repriced on and the base the commission scale is quoted against, so it is kept and published in result_pols(). On the anchor cell P_a = 12 x 974 = 11,688.

The annualization is [std] in the same sense as before: mode discounts are insurer-set and unpublished [S1][S7][S9][S14], so twelve months of premium is what a year of cover costs whatever the mode.

pols_if_init()[source]#

l(0) = 1: the model point is one policy, projected on an expected basis.

Survivorship multiplies the per-policy cash flows; no aggregation logic is specified in the technical notes and none is implemented.

pols_if(t)[source]#

l(t): the in-force probability at the start of policy month t.

pols_if_init() at t = 0, then the notes’ roll-forward l(t+1) = l(t)(1 - q_m)(1 - w_m)(1 - d) plus any 復活 reinstatements. This is the weight on every cash flow of the same result_cf() row.

Note which rates appear in it: the two rates per unit time are the monthly mort_rate_mth() and lapse_rate_mth(), while the renewal decline is the one-off proportion decline_rate() and enters unconverted, in the single month the 保険期間 ends.

It is continuous across a renewal boundary: a 更新 reprices the contract, it does not re-issue it [S1][S4], so there is no reset to 1 and no new cohort. Defined one month beyond the last projected month, at t = proj_len(), where it is the survivors whose cover expires at the ceiling — on the anchor cell l(600), the fraction of the cohort still in force after fifty years and four repricings. That is not a tail state: nothing is paid and nothing runs off, the cover simply ends [S1][S8][S10][S14].

pols_if_at(t, timing)[source]#

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

The notes’ processing order is death, then ordinary lapse, then the renewal decline — steps 3, 4 and 5 — and each timing reads the population the next decrement is taken from:

"BEF_DECR": l(t), the start of the month, before any decrement; the same number as pols_if() and the weight on that month’s cash flows.
"BEF_LAPSE": after deaths, before ordinary lapse.
"BEF_DECLINE": after ordinary lapse, before the renewal decline. Equal to "AFT_DECR" in every month that is not a renewal boundary, which on a 更新型 point is 599 months out of 600.
"AFT_DECR": after all three decrements — the end-of-month state, before any 復活 reinstatement is added back by pols_if().

Zero outside 0 .. proj_len() - 1: the cover has not started or has ended.

pols_death(t)[source]#

D(t) = l(t) q_m(t): expected death and 高度障害 claims in policy month t.

One decrement covering both, because the table includes 高度障害 [REG-R20] and the contract pays once and terminates on either event [S1][S8]. The monthly rate: a month’s claims are a twelfth of a year’s cover, not a year’s.

pols_lapse(t)[source]#

Ordinary lapses at the end of policy month t, from the survivors of mortality.

Pays nothing — there is no 解約返戻金 at any duration [S1][S4][S8] — so this moves pols_if() and nothing else. With the 復活 module on, these lives flow into pols_lapse_pool() rather than leaving for good.

pols_decline(t)[source]#

Renewal declines at the end of a boundary month, after ordinary lapse.

Zero in every month that is not the last month of a 保険期間, and zero on a 歳満了 point. In the one month it applies it dwarfs the other two exits, which are a single month’s worth apiece — that contrast is invisible on an annual grid, where the decline is compared with a whole year of lapse. Nothing is paid.

reinstate_rate_eff()[source]#

rho: the 復活 reinstatement rate actually applied — zero unless the module is on.

Keeping the effective rate in one cells is what lets pols_lapse_pool() and check_lapse_pool() carry the same ledger in both positions of the switch: with the module off the pool still tracks the lapsed-but-reinstatable population, and nothing is reinstated out of it.

reinstate_window_m()[source]#

W: the 復活 window in policy months, 12 reinstate_window.

Three years [S1], which on this grid is 36 months. The window is what pols_lapse_pool() tracks vintages over, and expressing it in months is what makes the pool age out on the anniversary of each life’s own 失効 rather than at the end of the third projection year — the error the annual grid could not make and this one can. reinstate_window stays a Reference in years because that is how the contract states it.

pols_lapse_pool(t)[source]#

lap(t): lapsed lives still inside the three-year 復活 window at the start of month t.

A stock, where pols_lapse() is the flow into it. Tracked by vintage rather than as one blanket balance, because the window runs from each life’s own 失効 and a single indicator would drop a whole cohort a month early or late:

lap(t) = sum over s in [max(0, t - W), t - 1] of pols_lapse(s) (1 - rho_m)^(t - 1 - s)

with W = reinstate_window_m() = 36 months [S1]. The vintage index s is the same 0-based month index as t, so the sum is empty and lap(0) = 0. Renewal declines never enter it: a declined renewal is an expiry, not a 失効, and there is nothing to reinstate.

The monthly grid carries 36 vintages where the annual grid carried three, which is the point of tracking them: a life that lapses in month 5 leaves the window in month 41, and no blanket balance indexed by projection year can say that.

reinstate_rate_mth()[source]#

rho_m: the monthly reinstatement rate, 1 - (1 - rho)^(1/12) [std].

reinstate_rate is quoted per annum like every other behavioural rate in this model, so it is converted on the same effective convention as mort_rate_mth() and lapse_rate_mth() rather than applied twelve times over. Zero unless the module is on, which is what keeps the pool ledger closing in both positions of the switch.

pols_reinstate(t)[source]#

Reinstatements out of the pool into pols_if(t + 1): lap(t) rho_m.

復活 is available for three years against arrears at 年6% compound [S1], on evidence of health [S8]. The arrears are not monetized — see the Space docstring — so the module is a persistency effect only. Reinstatement is the only event that restarts the suicide and contestability clocks [S1]; 更新 does not. Zero in the base run.

pols_lapse_expire(t)[source]#

Lives leaving the pool in month t because their three-year window has run out.

The vintage that lapsed in month t - W, net of the reinstatements taken out of it along the way, and zero while t < W, when no vintage has aged out yet. They are gone for good: after the window there is no 復活 [S1].

wop_inc_rate_mth()[source]#

The monthly 別表4 waiver incidence, 1 - (1 - wop_inc_rate)^(1/12) [std].

wop_inc_rate is quoted per annum, so the two-state chain below — which now steps once a month rather than once a year — needs the monthly equivalent, on the same effective convention as every other rate in this model. Zero unless the module is on.

wop_rec_rate_mth()[source]#

The monthly recovery rate out of the waiver state [std]; zero in every run.

1 - (1 - wop_rec_rate)^(1/12), and wop_rec_rate is zero [std] because a 別表4 state is largely permanent — so this is zero too. It exists rather than being inlined as a zero so that a user who sets a non-zero recovery rate gets it converted on the same convention as the incidence beside it instead of applied twelve times a year.

wop_waived_frac(t)[source]#

The fraction of in-force policies with premiums waived at the start of month t.

A two-state incidence chain [std], u(t+1) = u(t)(1 - rec_m) + (1 - u(t)) inc_m, stepping once a month and starting from u(0) = 0. The trigger is an accident on or after the 責任開始時 producing a 別表4 state within 180 days [S1][S8][S12][S14]. 別表4 is a materially lower bar than the 別表3 test for 高度障害 — loss of one eye, deafness in both ears, loss of one limb at the wrist or ankle [S1] — so this incidence is not the 高度障害 incidence and must not reuse mort_rate(). It is also largely permanent, which is why wop_rec_rate is zero [std].

wop_inc_rate = 0.0008 is an arbitrary placeholder: no retrieved document gives a 別表4 accident-disability incidence, the FSA and industry statistics in the source set do not publish waiver experience, and no observed range exists to quote. It is not derived from mort_rate() and must not be — 別表4 is a different and much lower bar than the 別表3 test the mortality table’s 高度障害 loading covers, so a number scaled off q would be a false derivation dressed as one. The module is off in the base run; it is live only on model point 7, where the two-state chain and its effect on pols_payer() are what is being shown.

While the waiver runs, premium income stops and cover continues [S1]; mortality and lapse are assumed independent of the waiver state [std], which is what lets the waived population be carried as a fraction rather than as its own decrement. Zero unless the module is on.

pols_waived(t)[source]#: In-force policies whose premiums are waived in policy month t; zero in the base run.

pols_payer(t)[source]#

In-force policies actually paying premium in policy month t.

l(t) less the waived fraction. Equal to pols_if() unless the 保険料の払込の免除 module is on.

ln_cap_binds()[source]#

Whether the リビング・ニーズ特約 cap would reduce a single-contract payment.

sum_assured() > ln_cap, a strict inequality, and False on every shipped model point. The ¥30,000,000 cap is per insured, aggregated across all of that insurer’s contracts [S1][S7][S8][S12] — not per contract — so inside the composite’s ¥1,000,000-¥30,000,000 envelope it is exactly reached at the ceiling and never reduces anything. A model reporting the cap biting at SA = 30,000,000 has a strict-versus-weak inequality error; a model applying it per contract has misread the clause. Model point 9 sits exactly on the boundary and must come back False.

ln_amount()[source]#

A: the accelerated amount under リビング・ニーズ特約, min(SA, cap).

Zero unless the module is on. A full acceleration extinguishes the contract retroactively to the claim date, which is what this model implements; a partial one leaves a reduced contract in force at a reduced premium [S1][S7], which is a second transition and a model point re-parameterization rather than one benefit with two amounts. It cannot arise inside the composite’s envelope, so rather than approximate it ln_amount() rejects it by name.

ln_available(t)[source]#

Whether an acceleration can be claimed in policy month t.

The rider is barred within one year of a non-renewable expiry [S1][S7][S8], which on this grid is the last twelve months of the projection, t >= proj_len() - 12 — and only those, since every earlier expiry on a 更新型 point is followed by a renewal. On a 更新型 cell the bar therefore bites only in the ceiling term.

The monthly grid states this bar as the contract states it. The annual grid could only approximate a one-year bar by barring the whole final projected year, which is the same length by coincidence of the grid rather than by reading the clause; here the twelve barred months are the twelve months the contract names.

ln_share(t)[source]#

a(t): the share of the month’s decrement arriving as an acceleration [std].

Modelled as a split of the existing death-and-高度障害 decrement rather than as an additional incidence, which is the same ruling the notes make for 高度障害: an acceleration is a re-timing and re-pricing of the death benefit, not a second claim, and a separate incidence on top would double-count it. The trigger is a six-month prognosis, not the twelve months of UK terminal illness cover [S1][S7].

ln_take_up = 0.10 is an arbitrary placeholder, and the honest defence of it is not a rationale but the switch: no retrieved document gives an acceleration take-up for any Japanese carrier, no observed range can be quoted, and nothing in the sources bounds it. A round tenth was chosen because it is visibly round — a number no reader can mistake for an estimate. The module is off in the base run, so the worked example and every figure this model publishes are independent of it; it is live only on model points 6 and 9, where what is being demonstrated is the mechanics of splitting the decrement and never the level of the split.

ln_payout_pp(t)[source]#

The リビング・ニーズ特約 payment per accelerated claim in policy month t.

A - A i_ln / 2 - six months' premiums on A [S1][S7][S8][S12]: the amount is discounted, unlike a UK terminal illness payment, which is the economic reason the rider can be offered without a separate premium. The premium element is pro-rated by A / SA [std], which is exact on the full acceleration this model implements.

ln_interest_rate = 0.02 is an arbitrary placeholder in the same sense. The contract fixes the rate only by reference — the insurer’s rate current at the claim [S1][S7] — and no retrieved document states a level or a range for it. What can be said positively is the size of its effect and nothing more: the rate enters halved, so 2% removes exactly 1% of A and the whole parameter moves the payment by 0.5% for every percentage point. The module is off in the base run, which is the only defence the number has.

premiums(t)[source]#

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

prem_due_pp() — the instalment the mode makes fall in this month — on the policies actually paying, pols_payer(), which is pols_if() unless the waiver module is on.

The grid retires a [std] the annual model had to carry. On an annual step the whole year’s premium was collected in advance from lives that might exit in month two, and the notes offset that overstatement against an end-of-year claim timing that understated by about the same amount, declaring the pair matched and warning against a further half-year adjustment. Here a policy that lapses in month two pays two months of premium and its claim falls in the month it arises, so neither approximation is made and neither needs an offset. What remains is a within-month timing convention only: premium at the start of the month, claims at the end of it.

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

Benefit outgo at the end of policy month t, by kind; the total when kind is omitted.

"DEATH": the sum assured on the month’s death and 高度障害 claims, SA (1 - a(t)) D(t). One decrement, one benefit: either event terminates the contract and the other is then not paid [S1][S8].
"LIVING_NEEDS": the discounted リビング・ニーズ特約 acceleration on the share a(t) of the same decrement. Zero in the base run. It is a split of the death benefit, never an addition to it.
"LAPSE": zero, always. There is no 解約返戻金 and no paid-up value at any duration [S1][S4][S6][S8][S9][S10][S13][S14]; the kind exists so that the zero is stated rather than left to inference. One carrier in eight writes this design with a surrender value [S12], so the zero is a fact about the composite and not about the product class.

claim_expenses(t)[source]#

ec D(t): the claim handling expense on the month’s claims [std].

¥30,000 per claim, uninflated, on the whole decrement whether the benefit is paid as a death claim or accelerated. Kept out of expenses() because the notes’ worked example prints the two as separate columns.

inflation_factor(t)[source]#

The expense inflation factor in policy month t [std], (1 + pi)^(y(t) - 1), pi = 1%.

Annual steps inside the monthly grid: maintenance expense inflates once a policy year, at the anniversary, rather than once a month. That is the library’s convention (IncomeTerm_JP_S does the same) and it is deliberate — a 1.0% p.a. assumption is an annual observation, and compounding it monthly would assert a within-year expense profile no source supports. Policy year 1 therefore carries a factor of 1.

expenses(t)[source]#

E0 and e_m(t): acquisition and inflating maintenance expense in month t [std].

¥15,000 per policy at issue — the acquisition charge falls in the first row of the frame, t = 0 — then ¥4,000 per policy per year taken as 4,000 / 12 a month and inflating at 1.0% a year, both at the start of the month. No Japanese public source supplies either level.

No acquisition expense is charged at a 更新. A renewal is not new business — no new 保険証券 is issued and no 告知 is taken [S1][S4] — so the t = 0 charge is the only one, however many times the contract renews. ¥4,000 a year against ¥11,688 of annualized premium is a third of the first term’s load, which is why the notes rate the [std] 1.0% inflation rate a poor assumption to leave unexamined.

comm_init_pp()[source]#

c0: initial commission per policy issued [std], 50% of the first year’s P_a.

Paid upfront at issue. With the acquisition expense it is ¥20,844 of outgo in the first month of the anchor cell against one month’s ¥974 of premium on the same row, which is the deep new business strain the protection shape starts from — and it is deeper here than on the annual grid, where a whole year’s ¥11,688 sat on the same row to meet it. The strain is the same money either way; the monthly grid shows when it is actually unfunded. No document in the source set discloses a Japanese commission scale, so both this and comm_renewal_rate are levels chosen for the reference implementation.

comm_new_term(t)[source]#

Commission paid at a 更新 [std]; zero in the base run.

A renewal is not new business [S1][S4], so the base run pays no acquisition commission on a renewed term. That is a choice and not a fact: no document in the set discloses a commission scale at all, and a scale paying first-year rates on each renewed term would change the sign of the cash flow at t = 120, 240, 360 and 480. Set comm_new_term_rate to switch it on; it then falls in the first month of each term after the first, which on the 0-based monthly frame is t = (k - 1) 12n, and it is charged on the annualized premium P_a because that is the base a commission scale is quoted against.

commissions(t)[source]#

Commission outgo in policy month t [std].

The initial commission at t = 0, then 5% of premium income from t = 12 — the first month of policy year 2, not the second month of policy year 1 — plus any commission at a 更新 (off in the base run). The threshold is stated in months for the same reason the lapse table is read through policy_year(): the scale is quoted by policy year, and t >= 1 on this grid would start renewal commission eleven months into the first-year commission’s own period.

No clawback on early lapse is modelled: the notes record that no Japanese clawback evidence exists in the source set, so a clawback rule would be an invention rather than a standardization of something observed.

net_cf(t)[source]#

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

Premiums less claims, claim expense, maintenance and acquisition expense and commission. The notes’ own sign — they write + = inflow — which is also the library-wide convention, so there is no outgo-positive liability_cf companion to publish.

Lapse and the renewal decline contribute no term: they act only through pols_if(). The shape to expect is the protection shape seen a month at a time: a single very deep month at t = 0 carrying the whole acquisition cost against one month’s premium, thin positive months through the middle of each term, months turning negative as each 保険期間 runs out and the level premium falls behind the rising mortality cost, and a jump back into surplus in the first month of the repriced term. On a 年払 point the sawtooth is larger again, because eleven months in twelve carry no premium at all.

check_pols_roll_fwd_resid(t)[source]#

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

l(t) - l(t+1) - D(t) - lapses - declines + reinstatements, the notes’ identity with the 復活 module’s inflow carried as its own term so that the same residual closes in both positions of the switch. Non-zero would mean the decrements and the roll-forward have drifted apart — most easily by applying the renewal decline to the wrong population, since it is taken after mortality and after ordinary lapse.

check_pols_roll_fwd()[source]#

True when the in-force roll-forward closes in every projected policy 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_lapse_pool_resid(t)[source]#

The 復活 pool roll-forward residual in policy month t; zero everywhere.

lap(t) - lap(t+1) - reinstatements - window expiries + lapses. The pool is a stock with one inflow (pols_lapse()) and two outflows (pols_reinstate() and pols_lapse_expire()), and the vintage bookkeeping of the 36-month window is exactly where an implementation drops or double-counts a cohort — twelve times more so on this grid than on the annual one, which had three vintages to keep straight. Closes with the module off as well as on, since the pool is tracked either way.

check_lapse_pool()[source]#: True when the 復活 pool ledger closes in every projected policy month.

check_pols_payer_resid(t)[source]#

The premium-paying population residual in policy month t; zero everywhere.

l(t) - payers - waived. The waiver module carries the waived lives as a fraction of the in-force rather than as a separate decrement, which is only legitimate while the two partition l(t) exactly.

check_pols_payer()[source]#: True when payers and waived lives partition the in-force in every projected month.

check_prem_level_resid(t)[source]#

The premium-level residual in policy month t; zero everywhere.

P_a(t) - P_a(t-1) inside a 保険期間, and zero by definition in the first month of a term. The premium is level within the term and changes only at a 更新 [S1][S4][S8][S12]; a residual here means the premium is drifting with the policy year, which is what happens if the rate lookup is keyed on attained age rather than on the term’s entry age. On the monthly grid that failure mode is the more likely of the two, because age(t) now steps eleven times inside a term where the premium does not move at all — so this check is doing more work here than it did on the annual grid.

check_prem_level()[source]#

True when the premium is level within every 保険期間 of the projection.

Note that it checks prem_pp, the annualized pricing quantity, and not prem_due_pp(): on a 半年払 or 年払 point the amount falling due is zero in most months by design, and a level-premium check over that series would be asserting the payment mode rather than the repricing rule.

check_net_cf_resid(t)[source]#

The published cash flow statement’s ledger residual in policy month t; zero.

net_cf() less the sum of the columns of result_cf(), so a reader adding up the printed statement gets the printed total. It is the check that catches a benefit kind that exists in claims() but was never given a column — which would leave the statement silently short of outgo it is charging.

check_net_cf()[source]#

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

Tested against cash_tol, not the roll_fwd_tol the four decrement checks use. The wider tolerance is a property of what is compared: the other checks close an identity between cells evaluated in one expression, where the residual is exact to a unit or two in the last place of a count near 1.0, while this one re-reads yen amounts of order 1e5 back out of the result_cf() DataFrame, so the round trip through column construction leaves float64 rounding of order 1e-11 in absolute yen. cash_tol = 1e-8 is well above that noise and far below one yen, which is the smallest error a reader adding up the printed statement could observe.

result_cf()[source]#

Result table of cashflows, indexed by the 0-based policy month t.

The frame runs t = 0 .. proj_len() - 1, so it has proj_len() rows — 600 on the anchor cell, twelve to the policy year. pols_if is the start-of-month count, which is the weight applied to every cash flow on the same row. net_cf carries the notes’ own income-positive sign. claims_lapse is a column of zeros by product design — there is no 解約返戻金 — and is published rather than dropped; see the Space docstring.

To read it by policy year, group by duration: df.groupby(df.index // 12).sum() reproduces the annual statement, with the one difference that matters — premium and claims are now weighted by the population of each month rather than of each year.

result_pols()[source]#

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

The renewal machinery is only legible next to the decrements it drives, so term_index and prem_pp are printed here with decline_rate: a boundary month is the row where the decline rate is non-zero and the premium changes on the next row.

Both the annual rates and the monthly decrements are published, because a reader holding the notes needs the first and a reader checking the roll-forward needs the second: mort_rate and lapse_rate are the annual rates the assumption tables are stated on, mort_rate_mth and lapse_rate_mth the rates actually applied to the month.