Implementation Notes

Status: Draft, 2026-08-26. Built from products/temporaire_deces/technical-notes.md; the product it implements is specified in product-spec.md.

This is a mechanics demonstration, not a pricing or reserving result. The contractual mechanics are sourced — the attained-age revision rule and the published tarif de base annuel [S3], PTIA as an acceleration whose payment ends the contract [S1] [S2] [S3] [S6], PTIA cessation earlier than death cessation [S3], premium cessation on death and on PTIA [S3] [S7], the first-year suicide void R1, the absence of any surrender or reduced-paid-up value R3, and the fractionation loadings with their frais d’échéance [S1]. Every behavioural and experience assumption is a std standardization: no French insurer publishes a mortality table, a PTIA incidence rate, an expense loading, a commission scale or a lapse rate for this product [S1] [S2] [S3] [S6] [S7] [S8] [S9] [S12], and the homologated TH 00-02 / TF 00-02 tables are annexed to an arrêté and are cited by name rather than redistributed here R6 REG-R22 REG-R23. Replace the decrement and expense tables with company data before drawing any conclusion from the numbers.

Run it

python products/temporaire_deces/run.py
python products/temporaire_deces/run.py 2      # the level-premium variant

Three lines to the same thing:

import modelx as mx
model = mx.read_model("products/temporaire_deces/TD_FR_S")
model.Projection[1].result_cf()

Projection takes a point_id; Projection[1] is the worked-example anchor cell. result_cf() returns a tidy DataFrame with one row per month and one column per cash flow line; result_cf_annual() is the same frame summed into policy years, which is the view the technical notes’ worked example is stated on and the one to lay beside an annual-step model; and result_pols() is the decrement side beside them, with each annual rate published next to the monthly rate derived from it.

The time index. t is 0-based and counts policy months, the clock lifelib’s basiclife/BasicTerm_S and the other monthly models of this library run on: t = 0 is the first policy month and month t runs from time t to time t + 1. proj_len() is the number of projected months — the exclusive end of the frame — so result_cf() runs t = 0 … proj_len() - 1, has proj_len() rows and is built with lifelib’s for t in range(proj_len()). On the anchor cell proj_len_y() = 75 - 58 = 17 policy years and proj_len() = 12 × 17 = 204 months.

Because every contractual schedule here is annual, the policy year is derived and used as a lookup key: duration_mth(t) = t is the completed policy months, duration(t) = t // 12 the completed policy years, policy_year(t) = duration(t) + 1 the contractual 1-based label, and age(t) = issue_age + duration(t) the attained age — which steps at the anniversary, not monthly. Only the two policy-year-keyed CSVs read policy_year(t), and nothing is indexed by it; see Inputs are external files below.

Every model point here is new business at issue, so every frame starts at t = 0; there is no in-force offset. pols_if(0) = pols_if_init(), and pols_if(proj_len()) is the expiring cohort, defined for the closure identity and a weight on nothing.

The model and both its Spaces carry docstrings — model.doc describes the product and the projection basis, model.Projection.doc holds the full mapping between the technical notes’ symbols and the cells names, and model.Data.doc says what each input file is and, for the mortality table, what it is not.

The cotisation rises with attained age — the French delta

This is the one thing about the product that a reader arriving from Term_UK_S or Term_US_S will get wrong, and it is visible in the cash flows rather than buried in a parameter. The French default premium form is revisable: the cotisation is recomputed at every annual renewal from the tariff rate at the new attained age [S1] [S2] [S3] [S4] [S6] [S7] [S9] [S10]. So prem_pp(t) moves every year — and only at the anniversary: the tariff is re-read in the first month of each policy year and is flat across that year’s twelve months, so a 204-month frame carries seventeen distinct cotisations and not 204.

policy year	1	2	3	…	17
months t	0–11	12–23	24–35	…	192–203
attained age	58	59	60	…	74
prem_rate(t) [S3]	1,05 %	1,13 %	1,56 %	…	4,86 %
prem_pp(t)	1 575,00	1 695,00	2 340,00	…	7 290,00

What is actually collected in a month is prem_inst_pp(t), the instalment the elected fractionnement makes due: the whole cotisation in the first month of the policy year on the annual mode, a twelfth of it every month on the monthly one.

prem_pp(24) / prem_pp(12) = 1,56 / 1,13 = 1,380531 — a 38 % step from age 59 to 60 against a trend of about 8 % a year. That step is in the published grid, and a fitted curve smooths it away, so prem_rate is a table lookup and nothing else. Over the whole cover the cotisation multiplies by 4,6286, which is exactly r(74)/r(58) and does not depend on the capital at all — a one-line test of the entire premium engine.

The level alternative, constante, is a model point column and a std construction: no French standalone contract in the corpus writes a level cotisation [S1] [S2] [S3] [S6] [S7] [S9] [S10]. With level_premium = 0 it is derived by actuarial equivalence with the revisable stream over the whole cover period, on tariff survivorship — insured decrements only, no lapse — at tech_rate = 0,5 % std:

P_lev = tariff_prem_pv() / tariff_annuity() = 60 476,2476 / 15,449728 = 3 914,3891 €

prem_level_pp() takes level_premium directly where the model point supplies one (model point 3) and derives it where it does not (model point 2), so both branches ship.

The two forms do not collect the same projected premium total, and a test asserting that they do is testing the wrong identity. The equivalence ignores lapse; once lapses truncate the expensive late years the constante projection collects 36 367,46 € against the revisable 31 999,13 €. The identity that does hold is the discounted one on tariff survivorship, P_lev × 15,449728 = 60 476,25 €. Switching form moves projected premium income by +13,7 % and net_cf by +18,4 % with no change to a single claim, which makes it the largest structural lever in the model R11 R13.

prem_rate also carries tariff_drift, an experience re-rating of the class, at 0 % p.a. in the base run. Two of the eight carriers reserve an express right to reprice for class experience [S1] [S6] and the same carrier’s current page implies a level above its own retrieved grid [S3] [S4]; freezing the card at its retrieved vintage is what keeps the base run reproducible from cited data alone. A drift assumption is a premium-income assumption, not a mortality one.

PTIA is an acceleration, not an addition

Perte totale et irréversible d’autonomie pays the same capital, early, to the insured, and its payment ends the contract [S1] [S2] [S3] [S6] [S8]. Arithmetically that is one two-decrement table, not two covers: mort_rate and ptia_rate are dependent rates and therefore additive,

pols_if(t+1) = pols_if(t) × (1 − mort_rate_mth(t) − ptia_rate_mth(t)) × (1 − lapse_rate_mth(t))

so a life that leaves through the PTIA decrement is gone from pols_if and can never generate a death claim. An implementation using independent rates, 1 − (1−q_d)(1−q_p), gets 0.00479680 against 0.00480000 at t = 0 — immaterial there, material at older ages, and either way a convention that has to be declared.

The additivity is also why the two rates are converted to the month together. mort_rate and ptia_rate stay the annual rates the technical notes tabulate. What the monthly recursion applies is their sum converted at constant force, decr_rate_mth(t) = 1 − (1 − q_d − q_p)^(1/12), split back into mort_rate_mth and ptia_rate_mth in the ratio q_d : q_p. Converting each rate apart and adding the results is the tempting reading and it is wrong here for exactly the reason above: it is the sum the annual recursion applies, so it is the sum that has to compound back. The naive form gives a twelve-month insured survival of 0,9952029339 against 0,9952000000 — 2,6 × 10⁻⁶ of error in pols_if at the first anniversary and 1,0 × 10⁻⁵ by month 204 — and loses the exact ptia_rate_mth / mort_rate_mth = ptia_ratio that the acceleration ratio rests on.

check_decrement_closure() asserts the consequence at every t: claim events plus lapses plus survivors equal the original policy. It is built by direct summation over the exit cells with no reference to the recursion, so a PTIA life left in force or counted twice fails there rather than hiding inside a plausible-looking total.

PTIA cover also stops earlier than death cover, at ptia_end_age, in five of the eight retrieved carriers [S2] [S3] [S6] [S7] [S8]. The switch is a hard gate on the attained age rather than a taper: ptia_rate(t) is exactly zero from the first t with age(t) ≥ ptia_end_age(). Because the attained age steps on the anniversary, the gate closes on an anniversary too: on the worked configuration that is t = 84 … 203, the whole of the policy year at attained age 65 onwards. Model point 11 enters at exactly ptia_end_age, so its PTIA cover never attaches at all. check_ptia_gate() recomputes the gate independently of ptia_rate and asserts both.

The suicide exclusion never touches PTIA. Art. L. 132-7 voids the death cover for suicide in the first year R1 — “au cours de la première année du contrat”, so the exclusion covers months t = 0 … 11 in full and a monthly grid does not shrink it to month 0 — and PTIA is not death, so suicide_factor multiplies benefit_death_pp alone. Nor does the model carry the art. R. 132-5 immediate-cover ceiling of 120 000 €: that alinéa is confined to principal-residence loan cover R1 R2.

No cash value, anywhere

Art. L. 132-23 forbids both rachat and réduction on a temporaire décès R3. There is no account value, no surrender value, no reduced-paid-up state and no maturity value at any duration [S3] [S5] [S7] [S9] [S11], so a lapse is a pure decrement: it moves pols_if and pays nothing.

claims(t, "LAPSE") exists, returns zero, and appears in result_cf() as a zero column, because a non-zero lapse row is the pitfall a reader arriving from a US model with cash surrender values will import. A column of zeros states the product fact; a missing column would only hide it. check_no_cash_value() is trivially zero by construction and is published anyway — the failure it guards against is not an arithmetic slip but an edit, and a named check that must stay at zero makes that edit fail loudly.

The same statutory fact is why the whole of the exit machinery is lapse. The 30-day renonciation window REG-R29 [S1] [S2] [S3] sits inside the year-1 lapse rate std; there is no surrender charge, no dynamic surrender behaviour and no paid-up election to model.

The last projected year has no lapse

The notes’ processing order puts lapses at the end of the month, after both insured decrements. At the end of the final projected policy year the cover expires, and a lapse and an expiry are then the same event paying the same nothing. So lapse_rate(t) is zero through the whole of that policy year — months proj_len() - 12 … proj_len() - 1, 192 to 203 on the anchor cell — and the whole surviving population leaves as an expiry. The zero covers the year and not just its last month because the notes state the convention of a policy year: w(n − 1) = 0 std, under Lapse and in step 9 of the processing order. Zeroing only the final month would leave eleven months of 6 % lapse inside the final year and move the survivor figure away from the notes’ own. Read over the whole year it reproduces their split of the closure identity:

	deaths	PTIA	lapses	survivors	total
worked configuration	0,06737020	0,00516859	0,64859269	0,27886852	1,00000000

The survivor term is exactly what the annual-step model this replaced carried, being a pure anniversary quantity; the three exit terms are not, and the reallocation is the expected effect of the finer grid — a decrementing block reaches the claim decrements later in the year, so fewer lives leave through them and correspondingly more leave as a lapse. (The annual grid read 0,06939268 / 0,00536169 / 0,64637711 against the same 0,27886852.)

pols_if(proj_len()) is that survivor figure. It is read by check_decrement_closure() and by nothing else — never a weight on a cash flow — and result_cf() stops at t = proj_len() - 1. There is no pols_expiry cells, because the notes put l(12n) in the identity directly rather than naming the expiry as a decrement. Nothing in the cash flows moves either way.

The délai d’attente

A délai d’attente delays the start of cover: 12 months for illness-caused death and PTIA where the adhesion carried no medical formality, with the cotisations collected returned to the heirs on a death inside the window [S6]; 3 months at another carrier, waived for accidental death [S9]. Five of the eight retrieved carriers have none [S1] [S2] [S3] [S7] [S8], and the composite runs with waiting_period_y = 0 [S3].

Model point 9 switches it on for one year. The mechanics are cited, the arithmetic is std: inside the window a death claim pays prem_refund_pp(t), the cotisations actually collected up to and including the month of claim, in place of the capital, and a PTIA claim pays nothing. On a fractionated point that is now strictly less than the annual cotisation of the year of claim, which is both the literal reading of “les cotisations collectées” and the only one that stays a cash quantity; model point 9 pays annually, so its 296,00 € is unchanged. The window itself is counted in months, duration_mth(t) < 12 × waiting_period_y() — the unit the sources actually state it in (12 months at one carrier, 3 months at another), and exactly the old window for a whole number of years. The monthly grid makes a sub-annual window expressible for the first time; no shipped model point uses one, so no waiting_period_m column is introduced. The refund accumulates at nil interest std — no source gives a rate. The accidental capital is not suppressed inside the window, which is the [S9] waiver. The decrements are untouched throughout: the window changes what a claim pays, never who leaves.

Inputs are external files

The six input CSVs live in this directory, beside run.py — not inside the model folder. TD_FR_S/ holds nothing but formulas:

products/temporaire_deces/
  model_point_table.csv        <- inputs live here
  premium_rate_table.csv
  mort_table.csv
  lapse_table.csv
  freq_loading_table.csv
  benefit_schedule.csv
  run.py
  model.md
  product-spec.md              <- the documents this model implements
  technical-notes.md
  sources.md
  TD_FR_S/                     <- formulas only
    __init__.py                   (model docstring)
    _system.json
    Data/__init__.py              (reads the CSVs, once per model)
    Projection/__init__.py        (the by-policy projection)

This follows lifelib’s annuallife/TradLife_A, which keeps its input file beside the model and reads it at run time. It is the opposite of basiclife/BasicTerm_S, which stores its inputs inside the model through modelx’s IOSpec machinery — hence no _data/ directory and no embedded values here at all.

Read once, in Data

Projection is parameterized by point_id, so every Projection[N] is a separate ItemSpace with its own cells cache. Readers placed there would re-read every file for every policy. They live instead in an unparameterized Data Space, which Projection references as data — so each file is read once per model no matter how many policies are projected. A test counts the reads.

Data.input_dir() resolves the location from _model.path.parent when the model is read, so it works wherever the repository is checked out.

Reference	Cells	File
model_point_file	model_point_table()	model_point_table.csv
premium_rate_file	premium_rate_table()	premium_rate_table.csv
mort_table_file	mort_table()	mort_table.csv
lapse_file	lapse_table()	lapse_table.csv
freq_loading_file	freq_loading_table()	freq_loading_table.csv
benefit_schedule_file	benefit_schedule()	benefit_schedule.csv

The trade-off: the model is not portable on its own. Copy TD_FR_S/ without the CSVs and it will read fine, then fail on first evaluation. What you gain is that a diff of the model shows logic changes only, and an input can be swapped in place — point Data.mort_table_file at another same-schema file and the projection follows, with no formula change. Tests cover both halves of that bargain.

File	Contents	Provenance
model_point_table.csv	Twelve model points. Point 1 is the worked-example anchor cell (revisable / M58 / non-smoker / 150 000 € / cover to 75 / PTIA to 65 / annual). Points 2–12 exercise the level premium derived and given, all four fractionation frequencies, a surprime, the accidental option, PTIA running to the death-cover limit, a cell entering at ptia_end_age, a one-year délai d’attente, a 35-year run from age 30, and a 20 000 € capital	anchor cell std, the technical notes’ worked example
premium_rate_table.csv	The tarif de base annuel by attained age 18–74 under rate_id = maif_2019, as a decimal fraction of the capital, with a provenance column marking ages 66–74 as in-force rates only	[S3], a real published grid — the only complete French standalone temporaire décès rate card in the corpus. A 2019–2021 vintage: use it for shape, not for level [S3] [S4] [S10]
mort_table.csv	Annual death rates by attained age 18–74, with each row tagged in a provenance column	std Gompertz-form proxy 0.00400 × 1.09^(age − 58). Not a published or homologated table: TH 00-02 / TF 00-02 are annexed to an arrêté and are cited, never shipped R6 REG-R22 REG-R23. The 9 % slope is calibrated on the published grid’s own gradient and sits at the top of it — the grid compounds at 7,7 % a year over ages 42–58 and 8,98 % over the rated span 35 → 74 [S3] — and a tariff gradient is not a mortality gradient. The anchor a replacement must preserve is mort_rate at age 58 = 0.00400
lapse_table.csv	Annual lapse by policy year, 12 / 10 / 8 / 6 %	std, and no observed range exists — not one of the eight retrieved carriers publishes a lapse rate [S1] [S2] [S3] [S6] [S7] [S8] [S9]. Elevated for three years to absorb the renonciation window REG-R29, then flat
freq_loading_table.csv	The fractionation multiplier and the fixed annual frais d’échéance by payment frequency	[S1] — with the 1,30 € association subscription and the 3 % annuity conversion charge, the only disclosed charge figures in the whole corpus
benefit_schedule.csv	Benefit factors by schedule id and policy year; one schedule, constant, factor 1.0 in every year	[S1] [S2] [S3] [S6] [S7] [S8] [S9] — the capital of a French standalone temporaire décès does not amortize. The table exists so a decreasing shape can be dropped in; no source gives one, so none ships

How the time-like input columns are keyed

The model’s t is 0-based; the shipped inputs are not all keyed by it, and each column was decided by meaning rather than by name:

File	Column	Decision
lapse_table.csv	policy_year (1 … 4)	Contractual 1-based label — file unchanged. The rates stay annual; lapse_rate_base(t) reads them at policy_year(t) = duration(t) + 1, so months t = 0 … 11 take the 12 % of policy year 1 and the last row is clamped to from policy year 4 on. lapse_rate_mth(t) does the spreading
benefit_schedule.csv	policy_year (1 … 57)	Contractual 1-based label — file unchanged. benefit_factor(t) reads it at policy_year(t) = duration(t) + 1, clamped to the last row
freq_loading_table.csv	instalments	Not time-like. The number of cotisation instalments per policy year — 1 / 2 / 4 / 12 — which drives prem_cycle() and prem_inst_pp(t). The column shipped with the file all along; the monthly grid is what gave it something to drive
model_point_table.csv	waiting_period_y	An elapsed count, in contractual policy years — unchanged. A 1 is a one-year window, which is months t = 0 … 11: in_waiting(t) is duration_mth(t) < 12 * waiting_period_y()
model_point_table.csv	issue_age, cover_end_age, ptia_end_age	Attained ages, not points on the time axis — unchanged
model_point_table.csv	issue_date	Carried for identification, read by no formula — unchanged
premium_rate_table.csv, mort_table.csv	age	Attained age, read through age(t) = issue_age + t — unchanged
freq_loading_table.csv	prem_freq	Not time-like — unchanged

No CSV holds the model’s t under any name, so no input file’s values were shifted by the move to the 0-based index. What moved is the two lookups, which now go through policy_year(t) instead of passing t raw.

Modules that are off in the base run

Four constructions are implemented and switched off, so the base run reproduces the worked example while the machinery stays visible and testable.

Module	Switch	Off value	What it does
Tariff drift	tariff_drift	0.0	Multiplies the rate card by (1 + drift)^duration(t), an experience re-rating of the class [S1] [S6] [S7]. The exponent is completed policy years, because a re-rating is an annual act
Premium-shock lapse	shock_lapse_beta	0.0	M_shock = 1 + β·max(0, P(t)/P(t−12) − 1 − g0) with g0 = 0.10 — the ratio is between consecutive renewals, so the previous cotisation is read twelve months back. The revisable form hands the policyholder a rising bill, and the grid’s own +38 % step at age 60 [S3] is exactly where an affordability response would show; switched on it bites through the whole of policy year 3, months 24–35, and nowhere else
Selective lapsation	sel_lapse_lambda	0.0	Loads persisters’ mortality by 1 + λ·max(0, w_cum − w_ref) once cumulative lapse passes w_ref = 30 %, with w_cum read at the anniversary so the loaded mort_rate stays one annual rate for its policy year. Larger here than on a UK level-premium term policy, because cumulative lapse reaches 64,9 % over seventeen years
Accidental capital	acc_share	0.0	An additional capital (accident_multiplier − 1) × acc_share × B(t) on the accidental share of claims [S1] [S2] [S6] [S7] [S9] [S12], not a uniform uplift. No retrieved source gives an accidental share of deaths

The selective-lapsation cells short-circuits when sel_lapse_lambda is zero, and that is load-bearing rather than an optimization: the loaded death rate depends on the lapse path, the lapse path depends on the premium under the shock module, and on the constante form the premium depends on the survivorship the loaded rate would feed. The equivalence is therefore struck on mort_rate_base and ptia_rate_base — the tariff rates — which is both the actuarially right basis and what keeps the derivation acyclic.

Indexation on the PASS or an insurer rate [S1] [S2] [S6] [S7] is described in the sources and is not implemented: it reprices capital and cotisation together on an exogenous index, and refusal is definitive at three carriers [S2] [S6] [S7], so modelling it would add an absorbing state driven entirely by an assumption with no source.

Sign convention

net_cf is income positive — cotisations in, claims and expenses out — which is the notes’ own orientation and the library-wide sign. liability_cf publishes the same stream outgo-positive, liability_cf(t) = −net_cf(t) exactly, and both are columns of result_cf() so the identity is verifiable in the frame rather than only in prose. A Solvabilité II best estimate is Σ v(t) × liability_cf(t) over the relevant risk-free term structure, plus a risk margin REG-R1 REG-R2 REG-R4 REG-R5; nothing in this library discounts.

expenses is the notes’ total and includes commissions, which is published beside it because the notes’ worked-example table prints both. The commission is a part of the expense column, not a further line: net_cf subtracts expenses once and never commissions as well. The worked example fixes the reading — expenses(0) = 250 + 2,08 + 0,06 + 630 = 882,14 € in the first month, the maintenance term being one twelfth of the 25 € annual charge, and the last of those four is the 40 % initial commission on the whole annual cotisation collected in that month. The twelve months of policy year 1 total 904,22 €.

Naming

Cells follow lifelib’s basiclife/BasicTerm_S wherever that model has an analogue: pols_* for policy counts, plural nouns for cash flows, *_rate for annual rates and *_rate_mth for the monthly ones derived from them, *_pp for per-policy amounts, claims(t, kind) with an uppercase kind string, and pols_if_at(t, timing) for the within-month in-force reads. The technical notes use compact actuarial symbols; the full mapping lives in the Projection Space docstring. Seven cases needed care:

Notes	Cells	Why
P_tar(t), P_lev, P(t)	prem_tariff_pp / prem_level_pp / prem_pp	Three different amounts, one per cells: the tariff cotisation SA·r·f·φ, the level cotisation struck by equivalence on that same amount, and what is actually charged — either of those plus the fixed frais d’échéance F once. P(t) is the one that feeds premiums and the commission base; the equivalence is struck on P_tar
q_d(t), q_p(t)	mort_rate_base / mort_rate, ptia_rate_base / ptia_rate	The table rate and the rate applied after the selective-lapsation loading are different numbers; and the constante equivalence is struck on the tariff pair, which is what keeps it acyclic
B(t)	benefit_pp / benefit_death_pp / benefit_ptia_pp	B(t) is the contractual capital. What a claim actually pays differs inside a délai d’attente, where a death pays back cotisations and PTIA pays nothing
w(t) vs w_cum(t)	lapse_rate / lapse_cum	lapse_cum is a proportion of the original cohort, not a running total of lapse_rate, and the loading it feeds moves claims
expenses(t)	expenses / commissions / claim_expenses	expenses is the notes’ total and contains the other two; they are named because the worked example rebuilds a month from them line by line
P(t) vs P_inst(t)	prem_pp / prem_inst_pp	Library-wide prem_pp is the annual cotisation per policy, which is what the notes’ P(t) means and what the tariff produces; prem_inst_pp is the instalment the elected fractionnement actually collects in a month. Twelve monthly instalments sum to exactly one prem_pp, fee included
q_d(t) vs q_dm(t)	mort_rate / mort_rate_mth, ptia_rate / ptia_rate_mth, lapse_rate / lapse_rate_mth	The unsuffixed cells keeps the annual meaning the technical notes give it — the rate of the policy year containing month t — and the *_mth companion is the rate actually applied in the month. lapse_rate_ann is a retired name for exactly this reason

Two further names exist only because of the time index. policy_year(t) = duration(t) + 1 is the contractual 1-based label, and it is what the two policy-year-keyed CSVs are read at; keeping it as a named cells rather than an inline expression is what stops the 0-based t from being passed raw into a table whose first row is policy year 1. And duration_mth / duration / policy_year is the same triple Obseques_FR_S and ADE_FR_S already carry, so the three models on this chassis read alike.

The model point carries issue_date and benefit_shape, and neither drives a formula: on the différence de millésime basis a projection on policy years needs issue_age and nothing else, and only the constant benefit shape has a shipped schedule. Both are exposed as documented cells rather than dropped, because the notes’ model point attribute table lists them and a silently missing column is worse than an inert one.

Standardizations used

Everything in this list is std: the whole mortality table and its 9 % Gompertz slope; ptia_ratio = 0.20, which has no source at all and is the assumption in the model most in need of one; the lapse duration table, for which no observed range exists; the suicide factor 0.98 and its restriction to year 1 and to death claims; acquisition expense 250 €; maintenance 25 € inflating at 2 %; claim expense 150 € per death or PTIA claim; initial commission 40 % of the first-year cotisation and renewal 5 % from year 2; the technical rate 0,5 % used only for the constante equivalence and never to discount a published cash flow; the whole constante form, since no French standalone contract in the corpus writes one; the additive dependent-rate convention and the death-and-PTIA-before-lapse processing order; the constant-force conversion of every annual rate to the month, taken on the combined insured decrement and split in the rates’ own proportion, since no retrieved French source states a conversion convention for any decrement; the collection of the cotisation in prem_instalments equal instalments on the mode’s own cycle, fee included; the expense inflation stepping by policy year rather than compounding continuously; the zero lapse rate in the final policy year; the délai d’attente arithmetic and its nil-interest refund; acc_share = 0, tariff_drift = 0, shock_lapse_beta = 0 and sel_lapse_lambda = 0; and the model points themselves.

The only quantities in the model that are not standardizations are the tariff grid [S3], the fractionation loadings and frais d’échéance [S1], the constant benefit factor [S1] [S2] [S3] [S6] [S7] [S8] [S9], the zero lapse benefit R3, and the structural rules — attained-age revision, PTIA acceleration and cessation, premium cessation, the first-year suicide void, and expiry with nothing payable.

Tests

tests/test_temporaire_deces_fr.py asserts the twelve months of the notes’ first policy year and every one of the seventeen rows of their policy-year table, read off result_cf_annual(), to the cent and pols_if to six decimals; the totals at full precision; the level-premium variant’s five printed years and its P_lev = 3 914,3891 € reached two independent ways and unmoved by the conversion; the closure identity’s four-way split; that twelve monthly rates compound back to exactly the annual ones and that the in-force at every anniversary is what the annual recursion gives; that result_cf_annual() is the monthly frame regrouped and not a second projection; that each annual contract term lands on the policy year rather than inside it; and one test per listed modeling pitfall — the revisable cotisation moving with attained age, PTIA never paid twice, PTIA cover stopping first, the additive dependent-rate convention, the absence of any surrender value, the différence de millésime age basis, the tariff grid’s unsmoothed +38 % step, the suicide factor applying only to death and only in the first year, the premium-cessation rule applied once, expiry with no tail state, the two premium forms not collecting the same total, rating_factor never reaching the capital, the fractionation loading and fee not being double-charged, and the accidental option having no effect at acc_share = 0.

Its month-level golden dictionary is keyed by the 0-based t (t = 0 … 11) and its policy-year one by the contractual 1-based label (1 … 17), and it pins the frame directly: list(df.index) == list(range(204)) with proj_len() == 204 and proj_len_y() == 17, and len(result_cf_annual()) == 17. tests/test_model_conventions_fr.py asserts the same library-wide frame rule for every model point of every model — index name t, index[0] >= 0, contiguous, and index[-1] == proj_len() - 1.

python -m pytest tests -q