The Pflege_DE_S Model

Reference liability cash flow model for the German Pflegerentenversicherung.

Pflege_DE_S is the executable counterpart of products/pflegerentenversicherung/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows, undiscounted, for a single-policy model point of a German private long-term-care annuity — a Pflegerente graded by the five Pflegegrade of §§ 14, 15 SGB XI, with full Beitragsbefreiung im Leistungsfall, on a monthly grid running to a terminal age of 110.

Three things make this the Pflegerente model rather than a translated disability one.

The benefit is a multi-state ledger, not a single decrement. The state space is {aktiv, PG1 … PG5, storno, tot}. A life enters care at a grade drawn from inc_share, deteriorates towards PG5, recovers towards PG1 and out to aktiv, and dies from every state at a grade-increasing multiple of active-life mortality. The paying state therefore has three exits, not one: death, a Herabstufung to a lower insured grade, and a Herabstufung out of the insured grades altogether, on which the annuity stops and the Beitrag revives. A model that treats “in claim” as one state exited only by death overstates the liability; one that treats every downgrade as a termination understates it. check_states() and check_waiver() assert the ledger and the premium split that hangs off it, on every model point.

Grade and mortality are correlated, and the highest-paying state is the shortest-lived. mort_mult is a multiple on the force of active mortality — 1.5 at PG1 rising to 9.0 at PG5 — so the annuity in payment runs three to five years, not the fifteen to twenty a healthy-life annuity would at the same age. Pricing this benefit on an annuity table would be prudent in exactly the wrong direction. The consequence for the code is that the annuity is weighted on esc_pg(t, g) grade by grade and never on an average benefit percentage applied to an average survival curve.

The premium is a priced quantity and the projection is not. Where premium_mth is 0.0 on the model point, the level monthly Beitrag is struck by equivalence on the first-order (erster Ordnung) bases — every rate carrying its prudence margin, the sexes blended 50 / 50 because sex may not enter a German premium, and no lapse — discounted at the Rechnungszins. That engine is the tar_* cells, it is the only place a discount rate appears, and check_prem_equiv() closes it from the tariff ledgers rather than from the closed form.

Spaces. The model contains two:

Data

Reads the nine 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, the worked example’s anchor cell. 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: plain 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, which are the contract’s own grid rather than a refinement of an annual one: the Pflegerente is a monthly annuity, the Beitrag a monthly instalment, and the Pflegegrad can change in any month. t is the policy month index, 0-based; the frame starts at duration_mth_init() — 0 for new business, the elapsed duration for an in-force point — and runs to proj_len() - 1, where proj_len() = 12 * (omega_age - age_at_entry) is the number of projected months, the exclusive end of the frame. The Beitrag, the Pflegerente and the per-policy expenses fall at the start of the month; transitions act over the month; surrender and death benefits fall at the end of it.

What is sourced and what is not. The contractual mechanics are cited: the statutory Pflegegrad trigger, the Beitragsbefreiung, the level guaranteed Beitrag adjustable only on the narrow § 163 VVG route, the 1,00 % Höchstrechnungszins of the DeckRV, the 25 ‰ Höchstzillmersatz, the § 169 VVG Rückkaufswert and Stornoabzug rules, and the unisex pricing constraint. Every biometric rate, every charge, every lapse rate and the premium itself is a standardization. No Bedingungswerk, Produktinformationsblatt, Tarifblatt or premium quotation for any German Pflegerentenversicherung was retrieved for this library, and DAV 2008 P — the German market’s standard multi-state Pflegetafel — is the property of the Deutsche Aktuarvereinigung, is not public and is not redistributed here; it is cited by name and the shipped tables are [std] proxies anchored so the worked example reproduces exactly, never calibrations of it. This model is a mechanics demonstration, not a pricing or reserving result. Replace the decrement, expense and surrender tables with company data before drawing any conclusion from the output.

Model points. Fourteen, covering both Leistungsstaffeln, all five payment modes including the Einmalbeitrag, a shortened Beitragszahlungsdauer, a Wartezeit with a Karenzzeit, a Leistungsdynamik, a Beitragsrückgewähr, a supplied premium with a Stornoabzug, two in-force points — one of them already in claim — and both ends of the observed entry-age band. Model point 1 is the anchor cell of the worked example in the technical notes.

Verification. tests/test_pflegerentenversicherung_de.py asserts the notes’ worked example to the cent and pols_if to six decimals, the equivalence premium and the actuarial values behind it, and one test per listed modeling pitfall.

Example

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