The Dep_FR_S Model

Reference liability cash flow model for French individual assurance dépendance.

Dep_FR_S is the executable counterpart of products/dependance/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for a single-policy model point of individual assurance dépendance: a lifetime monthly rente payable in arrears while a recognised state of dependence persists, a one-off capital d’équipement, the premiums refunded when dependence arises inside the carence, and expenses. Premiums are viagères and cease on recognition; there is no surrender value, no death benefit and no maturity.

This is a five-ledger multiple-state model. The health chain is autonome → dépendance partielle / dépendance totale → décès, and a fifth in-force but paid-up ledger, réduite, is reached only by lapse from eight years of premiums. Two features of that structure carry the product:

State-dependent mortality. A dependent life’s mortality is far heavier than a healthy life’s at the same age, and modelling it flat is this product’s first error. The model applies proportional hazards on the force — mort_partial_mult 1.75 and mort_total_mult 4.27 — so at attained age 85 the annual rates are 0.06179 healthy, 0.10562 in partielle and 0.23841 in totale. Flattening them while leaving the incidence basis unchanged raises lifetime claims by 159.7%. mort_total_mult is calibrated rather than picked: it is the value at which sojourn_total() returns 2.9989 years from exact age 84, against the “about three years” the CCSF reports for heavy dependents.

The *carence* and the *franchise* are different things and both are modelled. The carence runs from inception, is cause-specific (0 / 12 / 36 months by accident, illness, neurological or psychiatric illness), blocks the benefit and terminates the membership with a full refund of premiums. The franchise runs from recognition, is three months, and only delays payment. Removing the first raises lifetime claims by 3.99%, removing the second by 7.09% — different sizes, and different signs of error if either is applied in the other’s place.

The third structural feature is the mise en réduction: a policyholder who stops paying after eight full years keeps a reduced *rente totale* for life instead of nothing. Treating that lapse as an exit understates lifetime claims by 4.57% and drops a ledger that peaks at 8.27% of the original policy.

Spaces. The model contains two:

Data

Reads the eight input CSVs and holds their filename References. It takes no parameters, so each file is read once per model.

Projection

The by-policy projection, parameterized by point_id: Projection[1] is an ItemSpace projecting model point 1. It reaches the input tables through its data Reference, which resolves to the single Data Space.

The split matters for more than tidiness. Because Projection is parameterized, every Projection[N] is a separate ItemSpace with its own cells cache; readers placed there would re-read every file for every policy. In Data they are evaluated once, however many policies are projected.

Input data is external: CSVs in the model folder’s parent directory, read at run time rather than stored inside the model. The model folder itself holds no data, so the model and its inputs must travel together.

Projection basis. Monthly steps, matching the rente mensuelle à terme échu and the monthly premium. Policy month t is 0-based and runs 0, 1, …, proj_len() - 1, where proj_len() = 12 (110 - entry_age) is the number of projected months, 480 for the base cell — cover is viagère with no age limit, so what ends the projection is a [std] terminal age of 110, not the contract. Premium and expenses fall at the start of the month, benefits and transitions at the end of it, and the two revalorisations and any tariff revision at the start of months 12, 24, …

Model points come in four kinds. status = autonomous cells start the whole population in the autonomous ledger; status = partial and status = total cells start it in a dependent ledger at a stated claim duration; status = reduced cells start it paid-up on a reduced guarantee. An in-force portfolio needs all four.

What is sourced and what is not. The contractual mechanics are sourced: the two-state trigger and its AVQ and AGGIR grids, the rente partielle at half the rente totale, the capital d’équipement paid once per membership, the 0 / 12 / 36-month carence by cause with termination and refund, the three-month franchise, premium exonération from recognition, the eight-year mise en réduction and the CNP barème behind it, the absence of any surrender value, and the two separate indexations. Every rate is a standardization. No French LTC incidence or continuance table is public: the shipped prevalence curve is a [std] logistic fitted to two sourced DREES APA rates, the severity shares that turn public GIR prevalence into insured prevalence are [std], the state-mortality multiples are [std], the mortality proxy is a Gompertz shaped like a French population table and is not TH 00-02 / TF 00-02 or TGH05 / TGF05, and the lapse table has one indirect anchor. This model is a mechanics demonstration, not a pricing or reserving result. Replace the basis with portfolio experience before drawing any conclusion from the output.

Verification. tests/test_dependance_fr.py asserts the notes’ sixteen-month worked example to the precision the notes display, the policy-year-1 aggregates, the lifetime totals, and one test for each modelling pitfall the notes name.

Example

>>> import modelx as mx
>>> model = mx.read_model("products/dependance/Dep_FR_S")
>>> model.Projection[1].result_cf()