The Projection Space#

The by-policy projection of the WholeLife_JP_A 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 = 5            # or switch the default

t counts policy years, 1-based: t = 1 is the first policy year and t = proj_len() = omega_age() - age_at_entry() + 1 the last. There is no maturity date and no 満期保険金; the horizon is the terminal age of the mortality table, every remaining life dies in year proj_len(), and nothing is paid there but the death benefit. There are no tail states.

Input data

Inputs are external files: plain CSVs living in the model folder’s parent directory, products/whole_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.

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

Naming

Cells names follow lifelib’s basiclife.BasicTerm_S and savings.CashValue_SE wherever those models have an analogue — pols_* for policy counts, plural nouns for cash flows, *_rate for rates, *_pp for per-policy amounts, claims(t, kind) with an uppercase kind string, pols_if_at(t, timing) for the within-year in-force reads, cv_pp rather than av_pp because this is a cash surrender value and not an account value. The technical notes use compact actuarial symbols instead. The mapping is:

Notes symbol	Cells	Meaning
(none)	model_point()	The selected model point row
x	age_at_entry()	契約年齢 at issue, 満年齢
x + t - 1	age(t)	Attained age in year t
omega	omega_age()	Terminal age of the table
T	proj_len()	Projection length in years
m	prem_term(), prem_period()	保険料払込期間; 0 is 終身払
(none)	prem_end()	Last year a premium is due
SA	sum_assured(), sum_assured_at(t)	保険金額 at issue, in year t
P	premium_pp()	Annual premium
k	low_cv_rate()	解約払戻金支払割合
q(t)	mort_rate(t)	Mortality incl. 高度障害
(table q)	mort_rate_at_age(y)	Table rate at attained age y
(none)	mort_rate_base(t)	Table rate in policy year t
(none)	mort_be_factor()	Multiplier on the table rate
w(t)	lapse_rate(t)	Voluntary surrender rate
(table w)	lapse_rate_base(t)	Before spike and dynamics
s	lapse_spike()	Cliff spike applied at t = m
beta	lapse_beta	Dynamic-surrender slope
w_dyn(t) / w(t)	lapse_dyn_factor(t)	Dynamic-surrender multiplier
cumprem(t)	cum_prem_pp(t)	Premiums paid to year t
u(t)	default_rate(t)	Premium-default rate
l(t)	pols_if(t)	In force at start of year t
l(t)(1-q), l(t+1)	pols_if_at(t, timing)	BEF_DECR/BEF_LAPSE/AFT_DECR
(paying cohort)	pols_if_pay(t)	In force and paying premium
lp(t)	pols_pay_bef_decr(t)	Payers after the default exit
(none)	pols_default(t)	Movers into the APL state
D(t)	pols_death(t)	Expected deaths in year t
S(t)	pols_lapse(t)	Expected surrenders in year t
(APL failure)	pols_apl_exit(t)	Exits on APL exhaustion
(loan excess)	pols_loan_exit(t)	Exits on loan excess
i_cv	i_cv	Cash-value basis rate
i_std	i_std	Reference valuation rate
i_L	i_loan	APL / 契約者貸付 rate
alpha	acq_dedn_rate	Acquisition-deduction rate
(none)	disc_factor(), disc_factor_std()	1 / (1 + i)
A(y)	epv_death(y)	Whole-life EPV of 1 at age y
a-double-dot(y, n)	annuity_due(y, n)	n-year annuity-due at age y
A(y), a(y, n)	epv_death_std(y), annuity_due_std	The same on i_std
pi	prem_net_level_pp()	Net level premium on i_cv
pi*	prem_net_level_std_pp()	Net level premium on i_std
W(t)	prosp_val_pp(t)	Prospective policy value
SC(t)	surr_charge_pp(t)	解約控除
V(t)	pol_val_pp(t)	Ordinary surrender value
CV(t)	cv_pp(t)	Payable 解約返戻金
k V(t)	cv_pp_susp(t)	Suppressed value at every t
(none)	cv_mult(t)	1 or k, by policy year
(reserve)	reserve_pp(t)	平準純保険料式 reserve
L(t)	loan_pp(t)	Main-cohort loan balance
L(t) by cohort	loan_apl_pp(t, s)	APL balance by entry year s
A(t)	apl_advance_due(t)	Premium advanced in year t
(trigger)	apl_fires(t, s)	APL continuation test
CV*(t)	apl_test_val(t)	Value the APL test runs on
(exhaustion)	apl_fail_year(s)	Year the cohort exhausts
(advances)	apl_advances(s)	Number of advances made
(none)	pol_loan_year()	Year the 契約者貸付 is drawn
(none)	pua_sum_assured()	払済保険金額 after conversion
P lp(t)	premiums(t)	Premium income
(SA - L)D, (CV - L)S	claims(t, kind)	Benefit outgo by kind
ec D(t)	claim_expenses(t)	Claim expense
E0, e(t)	expenses(t)	Acquisition and maintenance
(none)	inflation_factor(t)	Expense inflation factor
c0, c_r	commissions(t)	Commission outgo
(dividend)	dividends(t)	5年ごと利差配当 outgo
CF(t)	net_cf(t)	Net cash flow, income positive

Four names needed care.

The notes write V(t) for the ordinary, unsuppressed surrender value and CV(t) for the amount actually payable. pol_val_pp() is V and cv_pp() is CV, and cv_pp_susp() is the third quantity the notes need at t = m: k V(t) at every duration, which is both the value an instant before the step and the value the clawed-back APL cohort keeps for life. All three are one policy value times one multiplier — there is no second reserve run anywhere in this model.

L(t) is one symbol in the notes but two objects here. loan_pp() is the 契約者貸付 balance of the premium-paying cohort; loan_apl_pp() is the automatic premium loan balance of a cohort indexed by the year s it defaulted in. They are kept apart because the APL exhausts at a duration that depends on s, so collapsing the cohorts to an average balance would let early entrants ride on late entrants’ headroom.

expenses is acquisition plus maintenance only. The claim handling expense is claim_expenses(), a separate cells, deducted explicitly in net_cf() and published as its own claim_expenses column in result_cf(), exactly as the notes’ worked-example table prints it. This is the settled meaning across the three libraries, so an expenses column means the same thing in all of them.

mort_be_factor is the cells; mort_adj is the model-point column it reads. The cells name is the library-wide one for the multiplier that turns the shipped valuation table into the projection basis, and the column keeps the spelling it ships with, so a CSV written against an earlier revision still loads.

The 低解約返戻金型 cliff is a step, not a ramp

CV(t) = k V(t) for t < m and CV(t) = V(t) for t >= m, with k = 0.70 where the suppressed form is elected. The transition at t = m is a step: the ratio cv_pp(m) / (low_cv_rate() * pol_val_pp(m)) is exactly 1 / k, and anything between is an interpolation the contract does not have. A surrender occurring in policy year m is paid at the end of that year on the full value [std ordering]; the suppressed value applies to years 1 to m - 1. Both quantities exist at t = m and the model publishes both, cv_pp() and cv_pp_susp().

On a 終身払 point (prem_term = 0) the suppressed period runs for life and the step never happens, which is why one shipped model point is written that way: it is the one configuration in which the product’s signature mechanic is absent by construction.

Lapse is a funded event

Where the premium is unpaid and there is a surrender value, the insurer lends the premium against that value and applies it to the premium, and the contract continues. So a premium default is not a lapse: default_rate() moves policies out of the paying cohort into an APL state, and only the failure of the continuation test

apl_test_val(t) >= loan_apl_pp(t, s) + premium_pp() * (1 + i_loan)

terminates them. The test runs on the suppressed value, which is the whole point: on the anchor cell a default at t = 2 buys one advance at k = 0.70 and thirteen at k = 1.00. Running it on V overstates the headroom by more than a decade of in force.

The advance is not cash income. No cash reaches the insurer, so an APL year produces no premiums() entry and no renewal commission; a loan asset is created and shows up only as growth in loan_apl_pp() and as a deduction from every later benefit. net_cf() is unchanged by an advance in the year it is made.

The clawback survives the step. A cohort carried through the low period by unrepaid advances has by definition not paid those premiums, so [std] its value stays at k V(t) for ever and never steps up at m. apl_clawback switches that off, and the difference is sixteen years of in force on the anchor cell.

Modules that are off in the base run

Six 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:

Premium default and the APL, default_rate at 0 on the base points and 1% p.a. for 1 <= t <= m on model points 5 and 6, which run it on the suppressed and the ordinary form respectively.
契約者貸付, pol_loan_util at 0, with model point 7 drawing the contractual maximum at the fortieth anniversary and reaching the loan-excess termination in year 53 with the benefit floored at zero. The 9/10-while-paying and 8/10-once-paid-up caps are contractual and always applied.
Dynamic surrender on the 払戻率, w_dyn = w min(3, max(1, 1 + beta (CV/cumprem - 1))) with lapse_beta = 2, off unless the model point sets dyn_lapse. Model point 8 turns it on and sets the cliff spike to zero, so the spike is produced endogenously instead of imposed — a cross-check on the 15% [std] choice rather than a replacement for it.
The cliff spike itself, lapse_spike, 15% [std] on every point but 8. It is a behavioural assumption and nothing in any retrieved document quantifies it; the step in CV that provokes it is contractual, and the two must not be confused.
払済保険 conversion, pua_year, 0 except on model point 4. The contract stops paying premiums, the sum assured is replaced by (CV - L) / A(x + t) on the same single-premium basis, and the suppression switches off for the future — but the conversion is made on the suppressed value, so the resulting 払済保険金額 is permanently smaller.
5年ごと利差配当, dividend_type, none except on model point 9. The composite is 無配当; the participating variant declares a dividend out of investment margin every fifth year, here as div_spread times five years of the policy value [std], because the declaration basis lives in the unpublished 算出方法書 and no carrier publishes it.

mort_be_factor is the last lever, 1.00 on every point but 9. At 1.00 the base run is a valuation-table run, not a best estimate: 生保標準生命表2018（死亡保険用）carries a roughly-2σ prudential margin and an eight-year improvement allowance already inside it, and no retrieved source sizes either against current insured experience. Claims move proportionately with mort_be_factor; the terminal rate is held at 1 whatever it is set to, because omega_age is the table’s horizon and not an experience assumption.

責任準備金 is not 解約返戻金

reserve_pp() is the 平準純保険料式 policy reserve, on i_std and the same table, and it never produces a cash flow. It exists so that the notes’ identity

reserve_pp(t) - pol_val_pp(t) = surr_charge_pp(t)

can be asserted — which it can only because i_std defaults to i_cv. When the two basis rates differ the ordering can fail outright: with a 標準利率 below the pricing basis the statutory reserve exceeds the cash value by far more than the 解約控除, and in a deep 逆ざや the reserve can exceed even the sum assured. reserve_pp >= pol_val_pp >= cv_pp is not a model invariant and check_reserve_identity() does not assert it.

Sign convention

The notes’ 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 liability_cf companion to publish: one stream, one sign, one name.

Cells Descriptions#

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

sex()[source]#: The sex of the insured, M or F; the two are rated and tabulated separately.

age_at_entry()[source]#

x: the 契約年齢 at issue, 15 to 80.

満年齢 (man-nenrei, attained age) with the fractional year discarded at 契約日; the rating age then increments on each 年単位の契約応当日 rather than on the birthday, so a projection stepped on anniversaries steps it correctly by construction. The mortality table does not share this basis: 生保標準生命表2018（死亡保険用）is built for a 保険年齢 (nearest-birthday) basis, and the table is read here at the 満年齢 attained age with no adjustment [std], because no public mapping between the two exists. The resulting bias understates mortality by up to half a year of age.

sum_assured()[source]#

SA: the 保険金額 at issue, level for life.

One amount pays two benefits — 死亡保険金 on death and 高度障害保険金 on the disability state defined in the 約款’s 別表 — and paying the second extinguishes the contract. They are one decrement on one amount, never two.

prem_term()[source]#

m: the 保険料払込期間 in years as entered, with 0 denoting 終身払.

On a 終身払 contract there is no 払込満了 date, the 低解約払戻期間 runs for life and the cliff never occurs. Use prem_period() for the effective number of years.

prem_period()[source]#

m: the effective 保険料払込期間, proj_len() on a 終身払 contract.

The suppressed period is identical to the premium-paying period, so this is also the duration at which cv_pp() steps up where it steps up at all.

prem_end()[source]#

The last policy year in which a premium is actually due.

prem_period() normally; one year less than pua_year() where a 払済保険 conversion is elected, because the contract stops paying at the conversion.

premium_pp()[source]#

P: the level annual premium per policy, payable in advance in years 1 to m.

Level and guaranteed for the whole of 保険料払込期間 with no unilateral repricing right, which puts every year of it inside any defensible contract boundary. On the anchor cell the value is sourced: ¥14,580 a month is published for exactly that cell, and the annual figure is 12 times it [std] — no carrier publishes an annual-mode scale, so the modal discount a real 年払 rate would carry is not applied and the annual premium is slightly overstated. On the other cells it is a [std] scaling of the anchor’s published-premium-to-prem_net_level_pp() ratio, divided by 0.837 on the ordinary form, that being the one carrier’s published ratio between its suppressed and its ordinary scale for one identical cell.

low_cv()[source]#

Whether the 低解約返戻金型 form is elected.

A model point flag rather than a modelling switch: the suppressed and ordinary forms are separately priced products, and the suppression buys a materially cheaper premium in exchange for a 30% haircut on the value during the premium-paying period.

low_cv_rate()[source]#

k: the 解約払戻金支払割合, 0.70 during the 低解約払戻期間 and 1.00 on the ordinary form.

Stated identically at four carriers. It is a multiplier on one common policy value, not a second reserve basis: at duration 40, well past 払込満了, the suppressed and the ordinary product have identical surrender values.

apl_elected()[source]#

Whether the 自動振替貸付 is elected; the default at four of the seven carriers.

Election varies more than any other feature in the source set — opt-out at four, opt-in at one, absent at two — so this is a genuine product variable. The supervisory guideline requires the facility to be at the policyholder’s election with prompt notice, which is why it is a flag with a default and never an unconditional no-lapse rule.

default_rate(t)[source]#

u(t): the premium-default rate in policy year t; 0 in the base run.

A decrement out of the premium-paying cohort into the APL state, not a lapse: a policy does not lapse while the cash value can carry the premium. Zero where the APL is not elected, and zero once no premium is due.

pol_loan_util()[source]#

The fraction of cv_pp() drawn as a 契約者貸付; 0 in the base run.

There is no public take-up data of any kind, so the level is a [std] model point input. The contractual caps in loan_cap_rate() bind it whatever it is set to.

dividend_type()[source]#

The participation basis: none (the composite) or five_year.

無配当 is the composite default because it is the largest single group in the source set and because a dividend is an insurer-discretionary element rather than a contractual one. five_year is the 5年ごと利差配当 variant, declared out of investment margin every fifth policy year; see dividends().

lapse_spike()[source]#

s: the extra surrender rate applied in policy year m [std], 15% in the base run.

The step in cv_pp() at 払込満了 is contractual; the surge in surrenders at the step is a behavioural assumption and nothing in any retrieved document quantifies it. It is held as its own parameter so that setting it to zero and re-running reads its effect directly, which is the right way to challenge it.

dyn_lapse()[source]#: Whether the dynamic-surrender module is on; off in the base run.

mort_be_factor()[source]#

The multiplier on the table mortality rate; 1.00 in the base run.

1.00 is a choice, not a default: it means the base run is a valuation-table run, not a best estimate. 生保標準生命表2018（死亡保険用）carries a roughly-2σ prudential margin and a built-in eight-year improvement allowance, but no retrieved source sizes either against current insured experience, so no defensible single haircut exists. A production basis would sit below 1.00 and would move claims proportionately.

Read from the model point’s mort_adj column, which keeps that spelling; the cells carries the library-wide name for the factor.

pua_year()[source]#

The policy year at which 払済保険 is elected, or 0 for no conversion.

Off on every model point but one. The conversion is made at the anniversary pua_year() - 1, so the earliest meaningful value is 2.

is_paid_up(t)[source]#: Whether the contract is on the 払済保険 basis in policy year t.

omega_age()[source]#

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

109 for males and 113 for females on 生保標準生命表2018（死亡保険用）. It is a hard model parameter and not a rounding: projecting a whole life contract to 100, a U.S. habit, truncates the liability, and projecting to 120 invents one.

proj_len()[source]#

T = omega - x + 1: the projection length in policy years.

There is no maturity date, so the horizon is the table’s, not the contract’s. Every remaining life dies in year T and pols_if(T + 1) is zero; nothing is paid at the horizon other than the death benefit and there are no tail states.

age(t)[source]#: x + t - 1: the attained age at the start of policy year t.

mort_rate_at_age(y)[source]#

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

Read from mort_table.csv, a [std] construction anchored on quoted rates of 生保標準生命表2018（死亡保険用）rather than a copy of it; see Data. The rate already includes 高度障害, so a projection using it must not add a separate disability decrement. This is the rate the contractual cash-value construction uses, unadjusted: mort_be_factor is a best-estimate lever on the decrement, not a change to the 算出方法書 basis.

mort_rate_base(t)[source]#: The table mortality rate in policy year t, at attained age age(t).

mort_rate(t)[source]#

q(t): the mortality decrement applied in policy year t, 高度障害 included.

The table rate times mort_be_factor(), capped at 1. At the table’s terminal age the rate is held at 1 whatever mort_be_factor is: omega_age is the horizon of the table and a structural property of the projection, not an experience assumption, and scaling it would leave lives alive past the end of the table.

lapse_rate_base(t)[source]#

The base voluntary surrender rate in policy year t [std].

4% / 3% / 2%, with the last row of lapse_table.csv read for every later year. The shape is reasoned, not fitted: a 低解約返戻金型 owner who surrenders during the low period takes a 30% haircut on a value that is already below cumulative premiums, so early surrender is strongly suppressed. No carrier publishes a lapse curve by duration; the only public benchmark is an amount-weighted, all-product industry 解約・失効率 of 5.6%, used here as a sanity ceiling and nothing more.

cum_prem_pp(t)[source]#

cumprem(t): premiums paid per policy by the end of policy year t.

P min(t, prem_end()). The denominator of the 払戻率 the dynamic-surrender module keys off, and the quantity the product is sold on: the 低解約返戻金型 value crosses 100% of it shortly after 払込満了.

lapse_dyn_factor(t)[source]#

The dynamic-surrender multiplier on the lapse rate [std]; 1 in the base run.

min(3, max(1, 1 + beta max(0, CV(t)/cumprem(t) - 1))). The economically natural driver on a savings-shaped contract is the ratio of the value to the premiums paid, and on the anchor cell that ratio crosses 1 exactly at the cliff — so with the module on and lapse_spike at zero the surge at 払込満了 is produced endogenously instead of imposed. There is no public calibration evidence for the form or for beta.

lapse_rate(t)[source]#

w(t): the annual voluntary surrender rate applied at the end of policy year t.

The table rate, plus lapse_spike() in the year the suppression ends, times the dynamic multiplier, capped at 1. This is the annual rate; there is no monthly companion on an annual-grid model. A surrender is not a pure decrement here: it pays cv_pp() net of any loan.

disc_factor()[source]#

v = 1 / (1 + i_cv): the discount factor of the cash-value basis.

i_cv is [std] and derived rather than asserted. The 予定利率, 予定死亡率 and 予定事業費率 live in the filed but unpublished 算出方法書, so the library constructs the policy value in closed form and calibrates it to one carrier’s complete published surrender-value run. The calibrated rate lands below the 予定利率 that carrier disclosed fifteen years earlier, which is informative rather than embarrassing.

disc_factor_std()[source]#

v* = 1 / (1 + i_std): the discount factor of the reference valuation basis.

i_std stands for the 標準利率, whose current numeric value could not be established from any retrieved official document — the 安全率係数 table for the annual case is printed as an omitted table in the retrieved redline. It therefore defaults to i_cv [std], which is what makes the reserve identity exactly testable.

epv_death(y)[source]#

A(y): the expected present value at age y of 1 payable at the end of the year of death.

On i_cv and the shipped table, unadjusted by mort_be_factor. Recursive: A(y) = v [q(y) + (1 - q(y)) A(y + 1)], with A(omega + 1) = 0 and q(omega) = 1, so A(omega) = v and the recursion terminates at the table.

annuity_due(y, n)[source]#

a-double-dot(y, n): the n-year annuity-due of 1 per year at age y, on i_cv.

1 + v p(y) a(y + 1, n - 1), zero for n <= 0. Measured in years of premium, so SA A(x) / a(x, m) is an amount per year.

epv_death_std(y)[source]#: A*(y): epv_death() on the reference valuation rate i_std.

annuity_due_std(y, n)[source]#: a*(y, n): annuity_due() on the reference valuation rate i_std.

prem_net_level_pp()[source]#

pi = SA A(x) / a(x, m): the net level premium of the cash-value construction.

This is not the priced net premium and must not be read as one. On the anchor cell it comes out above the gross premium, which would be a negative expense loading and no real product carries one: the construction uses the valuation table’s margin-loaded q as a stand-in for the insurer’s unpublished 予定死亡率, and surr_charge_pp() absorbs the difference. It reproduces the contractual value; it is not a pricing model.

prem_net_level_std_pp()[source]#: pi*: the net level premium of the 平準純保険料式 reserve, on i_std.

prosp_val_base_pp(t)[source]#

W(t) on the premium-paying construction, before any 払済保険 conversion.

SA A(x + t) - pi a(x + t, max(m - t, 0)): the prospective net level premium policy value at anniversary t, which is the end of policy year t. W(0) = 0 by construction and W(T) = 0 because the table terminates.

pua_sum_assured()[source]#

The 払済保険金額 the contract converts to, or 0 where no conversion is elected.

(CV(p - 1) - L(p)) / A(x + p - 1) at the conversion anniversary, on the insurer’s own single-premium net basis. The conversion is made on the suppressed value, so a 低解約返戻金型 contract converted during the low period carries a permanently smaller paid-up sum assured than the same contract converted after 払込満了.

sum_assured_at(t)[source]#: The sum assured in force in policy year t: SA, or the 払済保険金額 after conversion.

prosp_val_pp(t)[source]#

W(t): the prospective policy value at anniversary t, conversion included.

The premium-paying construction until the 払済保険 election, then the single-premium value pua_sum_assured() A(x + t) of the reduced paid-up contract. The change of basis at the conversion anniversary is a contractual re-basing, not a roll-forward step, and check_pol_val_roll_fwd() excludes that one year for exactly that reason.

surr_charge_base_pp(t)[source]#

SC(t) on the premium-paying construction: the 解約控除 grading to zero at m.

alpha SA max(0, m - t) / m [std], an initial deduction of 0.90% of the sum assured grading linearly to nothing at 払込満了. On a 終身払 contract the grading has no end date, so the deduction is held flat at alpha SA for life — the limit of the same formula as m goes to infinity.

surr_charge_pp(t)[source]#

SC(t): the 解約控除 embedded in the surrender value at anniversary t.

Zero once the contract is on the 払済保険 basis: the deduction was taken at the conversion, and the paid-up contract is a single-premium contract with none left to take.

pol_val_pp(t)[source]#

V(t): the ordinary, unsuppressed surrender value at anniversary t.

max(0, W(t) - SC(t)). The floor is not decoration: W - SC is negative in principle at t = 0 and none of this model’s amounts may produce a negative payment. This is the one policy value from which the suppressed value, the 払済保険 conversion amount, the 契約者貸付 limit and the APL headroom are all derived.

pol_val_base_pp(t)[source]#

V(t) on the premium-paying construction, before any 払済保険 conversion.

Needed by pua_sum_assured(), which values the conversion on the pre-conversion surrender value and would otherwise be circular.

cv_mult(t)[source]#

The 解約払戻金支払割合 applying at anniversary t: k before the step, 1 after it.

k for t < m and 1 for t >= m, and the transition is a step. A surrender occurring in policy year m is paid on the full value [std ordering]; the suppressed value applies to years 1 to m - 1. Always 1 on the ordinary form and once the contract is paid up, and always k on a 終身払 contract, where the suppressed period runs for life.

cv_base_pp(t)[source]#: CV(t) on the premium-paying construction, before any 払済保険 conversion.

cv_pp(t)[source]#

CV(t): the 解約返戻金 actually payable at anniversary t, per policy.

cv_mult(t) V(t). Everything derived from the surrender value is suppressed with it — the 払済保険金額, the 契約者貸付 limit and the APL headroom are all computed off this number rather than off V.

cv_pp_susp(t)[source]#

k V(t): the suppressed value at every anniversary, step or no step.

Two things at once, and the notes need both. It is the value an instant before the step at t = m — the published pre-step figure — against which cv_pp() an instant after must stand in the exact ratio 1 / k. And it is the value a clawed-back APL cohort keeps for life, because a cohort carried through the low period by unrepaid advances has not paid the low-period premiums and the suppressed basis therefore continues to apply after the period ends.

reserve_pp(t)[source]#

The 平準純保険料式 policy reserve at anniversary t — a reference quantity only.

Accumulated net level premium with no Zillmer adjustment, on i_std and the same table, which is what 平成8年大蔵省告示第48号 prescribes for a level-premium 終身保険 with a fixed 予定利率. It never produces a cash flow. It exists so that reserve_pp - pol_val_pp = surr_charge_pp can be asserted, and that identity holds only because i_std defaults to i_cv; reserve_pp >= pol_val_pp >= cv_pp is not an invariant and is not asserted anywhere.

loan_cap_rate(t)[source]#

The contractual 契約者貸付 limit in policy year t: 9/10 while paying, 8/10 once 払込済.

Stated identically at three carriers, with the existing balance deducted first. It binds pol_loan_util() whatever that is set to.

pol_loan_year()[source]#

The policy year at which the 契約者貸付 is drawn, or 0 for no drawdown.

A model point column rather than a fixed Reference, because when the loan is taken decides whether the contract survives it: a small early draw is outgrown by the value, while a draw of the contractual maximum late in the run compounds at i_loan against a value growing at i_cv and reaches the loan-excess termination.

pol_loan_draw(t)[source]#

The 契約者貸付 drawn at the start of policy year t; zero in the base run.

A single drawdown at pol_loan_year() [std] of the elected fraction of the value at the previous anniversary, capped by loan_cap_rate(). There is no public take-up data of any kind, so both the timing and the level are standardizations; a revolving facility would be another input table.

loan_pp(t)[source]#

L(t): the 契約者貸付 principal and interest of the paying cohort at the start of year t.

L(t + 1) = (L(t) + draw(t)) (1 + i_L), compound, with interest capitalised into principal. Identically zero in the base run, where every benefit is therefore gross.

loan_fail_year()[source]#

The policy year in which the loan outgrows the value, or proj_len() + 1.

The 約款’s loan-excess termination: where loan and interest exceed the surrender value the insurer notifies for a top-up and, unpaid, the contract lapses. The balance at the start of year t is tested against the value at the previous anniversary — the amount actually available to settle it — and the notice-and-top-up period is not modelled [std]. Never reached where no loan is drawn, because a zero balance cannot exceed a non-negative value.

apl_advance_due(t)[source]#

A(t): the premium the APL would advance in policy year t, zero once none is due.

Once t > prem_end() no premium is due, so the balance rolls up on interest alone against a value that is still growing — which is why exhaustion after 払込満了 takes decades rather than years.

apl_test_val(t)[source]#

CV*(t): the surrender value the APL continuation test is run against.

The value computed as if the premium had been paid, which on the annual grid is the value at the end of year t [std]. With the clawback on — the correct treatment, since a cohort carried by advances has not paid its low-period premiums — that is the suppressed value at every duration; with it off the value steps up at m like any other. Running the test on V instead of on k V overstates the headroom by more than a decade of in force.

apl_fires(t, s)[source]#

Whether the APL continuation test passes in year t for the cohort defaulting in year s.

CV*(t) >= L(t, s) + P (1 + i_L) while a premium is due, and CV*(t) >= L(t, s) once none is. Stated the same way at three carriers. In policy year 1 the value cannot carry a premium on either form, so a default at s = 1 terminates at once.

loan_apl_pp(t, s)[source]#

L(t, s): the APL balance at the start of year t of the cohort defaulting in year s.

L(t + 1, s) = (L(t, s) + A(t)) (1 + i_L), with the advance made only where the test fired. Indexed by the entry year and not collapsed to a cohort average: the APL exhausts at a duration that depends on when the loan started, so an average balance would let early entrants ride on late entrants’ headroom and would move the termination year by decades.

apl_fail_year(s)[source]#

The policy year in which the APL cohort entering in year s exhausts.

proj_len() + 1 where it never does. The cohort leaves at the start of that year and the policyholder may claim the surrender value net of the loan, floored at zero because the loan can exceed the value.

apl_advances(s)[source]#

The number of premium advances the APL makes for the cohort entering in year s.

The single most instructive number the module produces: on the anchor cell a default at s = 2 buys one advance on the suppressed form and thirteen on the ordinary one, from the same default at the same duration on the same underlying policy value.

pols_default(t)[source]#

Policies moving out of the paying cohort into the APL state at the start of year t.

pols_if_pay(t) u(t). Zero in the base run, and zero in the year a loan-excess termination takes the whole paying cohort.

pols_pay_bef_decr(t)[source]#: The paying cohort exposed to the year-t decrements, after defaults and loan exit.

pols_if_pay(t)[source]#

The premium-paying cohort in force at the start of policy year t.

pols_if_pay(1) = 1 and pols_if_pay(t + 1) = pols_pay_bef_decr(t)(1 - q)(1 - w). Equal to pols_if() in the base run, where no policy ever enters the APL state.

pols_apl_in(t, s)[source]#

The APL cohort of entry year s carried into the start of year t, before the year-t test.

pols_default(s) in the entry year, then decremented by mortality and voluntary surrender like any other in-force policy, and zero from the year after it exhausts.

pols_if_apl(t, s)[source]#

The APL cohort of entry year s exposed to the year-t decrements.

The carried amount, or zero in and after the year the cohort exhausts: an exhausted cohort leaves at the start of the year and does not experience that year’s deaths or surrenders.

pols_apl_exit_at(t, s)[source]#: The APL cohort of entry year s terminating at the start of year t on exhaustion.

apl_entry_years(t)[source]#: The entry years of every APL cohort that can be in force in policy year t.

pols_apl_carried(t)[source]#

The APL cohorts carried into policy year t from an earlier entry year.

Kept apart from the entrants of year t, which are still inside pols_if_pay() at the start of the year and would otherwise be counted twice.

pols_apl(t)[source]#: The APL cohorts exposed to the year-t decrements, summed over entry years.

pols_apl_exit(t)[source]#: Policies terminating at the start of policy year t because the APL exhausted.

pols_loan_exit(t)[source]#: Policies terminating at the start of policy year t on loan-excess; zero in the base run.

pols_if(t)[source]#

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

The premium-paying cohort plus every APL cohort carried in from an earlier year. This is the weight on every cash flow of the same result_cf() row. It is 1 in the first policy year on a single-policy model point and 0 at proj_len() + 1, because the table terminates and every remaining life dies in the final year.

pols_if_at(t, timing)[source]#

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

"BEF_DECR": l(t), the start of the year, before anything happens; the same number as pols_if() and the weight on that year’s cash flows.
"BEF_LAPSE": after the APL and loan-excess terminations and after deaths, before surrenders — the notes’ processing order is death before lapse [std order], so this is the population surrenders are taken from.
"AFT_DECR": l(t+1), the end-of-year state, and zero at proj_len() because the table’s terminal rate is 1 and nobody survives the final year.

pols_death(t)[source]#

D(t): expected death and 高度障害 claims in policy year t, at the end of the year.

One decrement covering both benefits at one amount: the shipped table already includes 高度障害 inside the death rate, so adding a separate disability decrement would double-count. The リビング・ニーズ rider is an acceleration that reduces the sum assured by what it pays, so it is not an addition either and its incidence is zero in the base run [std].

pols_lapse(t)[source]#

S(t): expected voluntary surrenders at the end of policy year t.

Taken from the survivors of mortality — death before lapse [std order] — and paid on the surrender value at that anniversary, net of any loan. A surrender in policy year m is paid on the full value; the suppressed value applies to years 1 to m - 1.

premiums(t)[source]#

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

Carried on pols_pay_bef_decr(), never on the APL cohorts: an APL advance is not cash income. No cash reaches the insurer, a loan asset is created instead, and booking the advanced premium as income while also netting the loan off the later claim would count it twice. net_cf is unchanged by an advance in the year it is made. Zero from prem_end() + 1; nothing else about the contract stops there.

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

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

"DEATH": the 死亡保険金 / 高度障害保険金 paid at the end of the year of death, (SA - L) D(t) floored at zero, cohort by cohort because each APL cohort carries its own balance.
"LAPSE": the 解約返戻金 paid on voluntary surrender, (CV(t) - L) S(t) floored at zero, plus the residual value paid where an APL cohort exhausts or a loan outgrows the value, which is settled on the previous anniversary’s value net of the balance that broke the test.

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

claim_expenses(t)[source]#

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

¥20,000 per claim, uninflated. No carrier publishes an expense basis of any kind — the 予定事業費率 is named in the 保険契約者保護機構 boilerplate and never quantified — so every expense level in this model is a standardization. Published as its own claim_expenses column in result_cf() and deducted explicitly in net_cf(); it is not inside expenses().

inflation_factor(t)[source]#

The expense inflation factor in policy year t: (1 + pi)^(t-1) [std].

1.0% p.a., deliberately below the 3% a UK or U.S. model would carry: over an eighty-year whole-life horizon 1% compounds to 2.19 and 3% to 10.33, so importing a Western inflation assumption here produces a different product rather than a stressed one. There is no published Japanese expense basis to anchor either figure.

expenses(t)[source]#

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

¥50,000 per policy at issue, then ¥8,000 per policy per year inflating at 1%, both at the start of the year. The claim handling expense is not here: it is claim_expenses(), deducted separately in net_cf() and published in its own result_cf() column, which is how the notes’ worked-example table prints it too. Maintenance continues for life, not to 払込満了: that is the structural point of this product, a contract on which premiums stop after m years and obligations do not. There is no separate surrender expense; it is folded into maintenance [std].

commissions(t)[source]#

Commission outgo in policy year t [std].

90% of the annual premium at issue, then 3% of premium income in years 2 to prem_end(). Both levels are standardizations; no Japanese carrier publishes a commission scale. Renewal commission follows the premium actually collected in cash, so an APL cohort produces none [std], and none is paid after 払込満了 — a projection that keeps charging it there is charging commission on a premium nobody pays.

dividends(t)[source]#

The 5年ごと利差配当 declared at the end of every fifth policy year [std]; 0 in base.

div_spread times div_period years of the policy value, on the policies surviving mortality. The composite is 無配当 and this column is zero on every model point but one. The declaration basis is a 三利源 calculation inside the unpublished 算出方法書 and no carrier publishes it, so both the spread and the once-in-five-years timing are standardizations — the timing is the only part of it that is sourced, from the product name itself.

net_cf(t)[source]#

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

Premiums less death and 高度障害 claims, surrender benefits, claim_expenses(), maintenance and acquisition expense, commission and any dividend. The notes’ own sign, which is also the library-wide convention, so there is no outgo-positive liability_cf companion to publish.

The shape to expect is a deep new business strain in year 1, then a long positive stretch while the premium runs, then a single violent negative year at 払込満了 where the surrender value steps up by 1 / k and the surrender assumption spikes with it, and finally a run-off of claims and expenses against no premium at all. The cliff is the largest single feature of this stream and it is one year wide.

check_pols_roll_fwd_resid(t)[source]#

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

l(t) - l(t+1) less deaths, surrenders, APL exhaustions and loan-excess terminations. The last two are zero in the base run and are what makes the identity close when the modules are on: a policy that leaves because its loan outgrew its value has left for a reason that is neither a death nor a surrender.

check_pols_roll_fwd()[source]#

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

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 year that failed.

check_decrement_sum_resid(t)[source]#

The cumulative-decrement residual at policy year t; zero everywhere.

l(1) less every exit up to and including year t less l(t+1). At t = T it is the notes’ statement that the decrements sum to 1: because the table terminates, every policy leaves by one of them and l(T + 1) = 0, so there is no residual population and no tail state anywhere in this model.

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

check_pol_val_roll_fwd_resid(t)[source]#

The policy-value recursion residual at anniversary t; zero everywhere.

(W(t-1) + pi 1{premium due}) (1 + i_cv) - [q SA + (1 - q) W(t)] on the table rate, which is the retrospective form of the same prospective value and is what catches a mis-set prem_period or a discount factor applied on the wrong side. It is defined as zero at the 払済保険 conversion anniversary, where the value is re-based by the election rather than rolled forward.

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

check_reserve_identity_resid(t)[source]#

The 責任準備金-to-解約返戻金 residual at anniversary t; zero everywhere.

reserve_pp(t) - pol_val_pp(t) - SC(t), with the deduction floored at the reserve itself because the surrender value cannot go below zero. The whole difference between the two quantities is the 解約控除, which is precisely what 平準純保険料式 forbids the reserve to carry. Zero by definition when the two basis rates differ: the identity is a consequence of i_std = i_cv and is not asserted otherwise, because with a 標準利率 below the pricing basis the reserve exceeds the cash value by far more than the 解約控除.

check_reserve_identity()[source]#: True when the reserve exceeds the surrender value by exactly the 解約控除.

check_loan_roll_fwd_resid(t)[source]#

The loan roll-forward residual in policy year t; zero everywhere.

The 契約者貸付 balance and every APL cohort balance, each rolled L(t + 1) = (L(t) + advance) (1 + i_L) and compared with the balance the model actually carries. Identically zero in the base run, where there is no loan at all; non-trivial the moment either module is switched on, which is the point of it.

check_loan_roll_fwd()[source]#: True when every loan balance accumulates at i_loan in every year.

check_net_cf_resid(t)[source]#

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

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

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

result_cf()[source]#

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

pols_if is the start-of-year count, which is the weight applied to every cash flow on the same row. net_cf carries the notes’ own income-positive sign. expenses is acquisition and maintenance; the claim handling expense is beside it in claim_expenses, as it is in every model in the three libraries. dividends is a column of zeros on the 無配当 composite and is published rather than dropped, because the participating variant is a real product in the source set.

result_pols()[source]#: Result table of policy counts and decrement rates, indexed by policy year t.

result_val()[source]#

Result table of the policy value, the surrender value and the reserve, by t.

cv_pp is the amount payable and cv_pp_susp the suppressed value at every anniversary, so the step at 払込満了 and the value an instant before it can be read off the same table. reserve_pp is a reference quantity and produces no cash flow.