The RLV_DE_S Model

Reference liability cash flow model for the German Risikolebensversicherung.

RLV_DE_S is the executable counterpart of products/risikolebensversicherung/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for a single-policy model point of a German standalone term assurance — the Versicherungssumme paid as a Todesfallleistung on death inside the Versicherungsdauer, and nothing at all otherwise — on a monthly grid, undiscounted.

Three things make this the German model rather than a translated French or British one.

The customer is not billed the premium the contract guarantees. The tariff premium is the Bruttobeitrag, struck on prudent first-order Rechnungsgrundlagen, and it is the maximum the policyholder can ever be required to pay. What is billed is the Zahlbeitrag: the Bruttobeitrag less a declared Beitragsverrechnung, which is how § 153 VVG’s surplus entitlement is delivered on a product with no account to credit. The MindZV obliges the insurer to allocate at least 90 % of the Risikoergebnis to policyholders, and on a term product the Risikoergebnis is essentially the whole technical result, so the spread is wide: on the worked example’s anchor cell the Beitragsverrechnungssatz comes out at 0.4253 and the billed premium at 57,5 % of the guaranteed one. The model therefore publishes two premium streams — prem_gross, the guaranteed one, and premiums, the billed one that enters net_cf — and prem_rebate between them. A model carrying one premium stream cannot represent this product, and the Beitragsverrechnungssatz is derived from the surplus mechanic rather than assumed, because that is what it is in the real contract.

The tariff is unisex and the projection is not. Sex may not enter a German premium for contracts concluded from 21 December 2012, while the DAV 2008 T tables the tariff is built on remain sex-distinct, so every German term tariff is a blend at a mixing ratio the carrier chooses. mort_rate_tar prices on a 50/50 blend and mort_rate projects on the policy’s own sex, so the cross-subsidy appears in the cash flows instead of in the price: model points 1 and 2 differ only in sex, pay the same premium to the last cent, and have claim totals differing by a factor near two.

There is no cash value anywhere. § 169 Abs. 1 VVG confines the surrender-value duty to a life insurance whose insured event is certain to occur, which a term assurance’s is not, and § 165’s paid-up right collapses into the same nil through the minimum-benefit test. So the model has no account value, no av_pp_at, no surrender cells and no paid-up state, and claims(t, "LAPSE") and claims(t, "MATURITY") are structurally zero at every t. check_no_cash_value() asserts it on every model point rather than leaving it to prose. What is not true is that nothing accumulates: a level premium charged against a rising death rate builds a small Deckungskapital that peaks near the middle of the term and runs off to exactly zero at expiry, and res_pp_at publishes it as a pricing diagnostic. Concluding from “no Sparanteil” that there is no reserve is the modelling error this product invites, and check_res_roll_fwd() is what catches it.

Spaces. The model contains two:

Data

Reads the six 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. The time index t is 0-based and counts policy months from issue: proj_len() = 12 x policy_term is the number of projected months and the frame’s exclusive end, a new-business point opens at t = 0 and an in-force point at t = 12 x duration_y, so the frame is t = 12 duration_y … proj_len() - 1. The product is annual and stays annual: duration(t) = t // 12 and policy_year(t) = duration(t) + 1 are derived and never indexed by, and everything the contract puts on the anniversary stays there — age(t) = issue_age + duration(t), the Versicherungssumme schedule, the § 161 three-year window, the Beitragszahlungsdauer and the whole first-order equivalence, whose Bruttobeitrag, Nettoprämie, Beitragsverrechnungssatz and Deckungskapital are unmoved by the conversion. What the finer grid resolves is the timing: mort_rate and lapse_rate are the policy year’s annual rates and mort_rate_mth and lapse_rate_mth the monthly rates derived from them at 1 - (1 - r)^(1/12), so twelve of each compound back to the year’s rate and pols_if at every anniversary is the annual-step model’s own figure.

A Zahlbeitrag instalment on the Zahlweise’s own cycle, its collection cost and the renewal commission on it fall at the start of the month; a twelfth of the sum-related admin charge accrues each month on the opening in-force; acquisition cost and initial commission fall in month 0 and never on an in-force point, where they are sunk; death claims and the claim expense at the end of the month of death; lapses at the end of the month, after the death decrement; the expiry at the end of the last month t = proj_len() - 1, paying nothing. result_cf_annual() sums the monthly frame into policy years, which is the view the technical notes’ worked example is stated on.

What is sourced and what is not. The contractual mechanics are sourced, if only ever through inherited corroboration: the guaranteed Bruttobeitrag and the non-guaranteed Zahlbeitrag, the MindZV’s 90 % minimum allocation from the Risikoergebnis, the three-year Selbsttötung window of § 161 VVG and its substitution of a Rückkaufswert that is nil here, the absence of any surrender or paid-up value, the unisex rule, and the Höchstrechnungszins and Höchstzillmersatz the tariff is bounded by. Every price, charge, margin and behavioural level is a standardization. No German insurer publishes a mortality table, a Sicherheitszuschlag, an expense loading, a commission scale, a lapse rate or a Beitragsverrechnungssatz for this product, and the DAV 2008 T tables — DAV 2008 T NR and DAV 2008 T R — are the property of the Deutsche Aktuarvereinigung, are not public, and are cited by name rather than redistributed here. This model is a mechanics demonstration, not a pricing or reserving result. Replace the decrement and rate tables with company data, and the charge parameters with a real tariff’s, before drawing any conclusion from the output.

Model points. Fourteen, covering both premium forms, all four Zahlweisen, all three Versicherungssumme shapes, an in-force point opening at t = 12, a Nachversicherungsgarantie with two increments, verbundene Leben, a Risikozuschlag on an impaired smoker, the § 153-excluded non-participating tariff, an abgekürzte Beitragszahlungsdauer, and two boundary cells at the ends of the issue-age and term envelopes. Model point 1 is the anchor cell of the worked example in the technical notes.

Verification. tests/test_risikolebensversicherung_de.py asserts every row of the notes’ twenty-five-year worked example to the cent — on result_cf_annual() — and the twelve months of policy year 1 on the monthly frame beside it, pols_if to six decimals, the Bruttobeitrag 1 275,411882 € and the Beitragsverrechnungssatz 0,42527476 behind it, and one test per listed modeling pitfall.

Example

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