The BU_DE_S Model

Reference liability cash flow model for the German selbstaendige Berufsunfaehigkeitsversicherung.

BU_DE_S is the executable counterpart of products/berufsunfaehigkeit/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 standalone occupational-disability contract — a monthly BU-Rente while the insured is berufsunfaehig, a Beitragsbefreiung for the same period, and nothing at all otherwise — on a monthly grid over t = 0 ... proj_len() - 1.

Three things make this the German BU model rather than a translated disability rider.

It is a four-ledger multi-state chain with a return arc. aktiv (paying premium, exposed to inception, active-lives mortality and lapse) becomes leistungspflichtig (receiving the BU-Rente, premium-free, exposed to reactivation and to disabled-lives mortality), which on a Nachpruefung termination becomes a three-month run-off in which the annuity is still paid, and only then returns to aktiv. Death and lapse are the only absorbing exits, so inception, recovery and reactivation are internal transfers and must not appear in the closure identity. The run-off is § 174 VVG in arithmetic: the insurer stays liable to the end of the third month after the notice reaches the policyholder, so a recovery does not release the liability in the month it happens. check_runoff_roll_fwd() and check_dis_roll_fwd() assert both ledgers close.

The premium is quoted as two numbers. The Bruttobeitrag is the contractually guaranteed maximum, struck on Rechnungsgrundlagen erster Ordnung; the Zahlbeitrag actually charged is beitragsverrechnung times it, the anticipated Ueberschuss credited in advance under § 153 VVG through § 176. Both are published — premiums() is the gross stream and surplus_credit() the credit returned out of it — because a model carrying only one of them either assumes the credit is permanent or overstates collected premium by 1 / 0.70 - 1. No German BU rate card exists in this library’s source corpus, so the Bruttobeitrag is derived by an equivalence on a stated first-order basis rather than read from a table.

The premium is weighted by the premium-paying count, not by the in-force count. pols_prem(t) is pols_actv(t) plus the disabled cohorts still inside the Karenzzeit: charging premium to lives in claim silently deletes the Beitragsbefreiung, which is core cover and not an option.

Spaces. The model contains two:

Data

Reads the seven 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 holds nothing but formulas — no _data/, no IOSpec, no embedded values — so the model and its inputs must travel together, and a diff of the model shows logic changes only.

Projection basis. Monthly steps, matching the BU-Rente paid monthly in advance and the retail monthly premium. t is the policy month, 0-based: t = 0 is the first projected month — the month of inception for a new-business point, the valuation month for an in-force one — and proj_len() is the number of projected months, the exclusive end of the frame, so result_cf() runs t = 0 ... proj_len() - 1 and ends there — 444 rows on the anchor cell. Premium, the surplus credit, administration expense, the BU-Rente and the claim-maintenance cost fall at the start of the month; every state transition and the claim-assessment cost at the end of it.

What is sourced and what is not. The mechanics are the established German ones and each carries the instrument it must be checked against: the Berufsunfaehigkeit definition and its 50 % / six-month concretisation, the Anerkenntnis and Nachpruefung frame with its three-month run-off, the Beitragsbefreiung, the Brutto / Zahlbeitrag pair, the unisex rule, and the absence of any death, maturity or surrender benefit. Every level is a standardization. The DAV 1997 family (inception, reactivation and disabled-lives mortality) and DAV 2008 T are the property of the Deutsche Aktuarvereinigung, are not public and are not redistributed here — they are cited by name and the model ships anchored [std] proxies instead. No German insurer publishes a BU charge structure, lapse rate or rate card, and a pure risk contract carries no Effektivkosten disclosure, so the charges and the premium are [std] too. This model is a mechanics demonstration, not a pricing or reserving result. Replace the decrement, charge and premium bases with company data before drawing any conclusion from the output.

Model points. Thirteen, covering both premium forms, all four payment frequencies, an in-force active policy, an in-force policy already in claim, a Karenzzeit, an Endalter of 60, a Leistungsendalter below the Versicherungsdauer, the AU-Klausel switched on, a Risikozuschlag, a point with both escalation options off, and a premium override. Model point 1 is the anchor cell of the worked example in the technical notes, and model points 2 and 3 are one-attribute neighbours of it so that the unisex invariance and the occupational loading can be measured against it rather than inferred.

Verification. tests/test_berufsunfaehigkeit_de.py asserts the notes’ worked example to the cent and pols_if to six decimals, the derived annual Bruttobeitrag, and one test per listed modeling pitfall. tests/test_model_conventions_de.py asserts the house style, including delib’s two rulings: every model publishes check_net_cf(), and every input CSV but the model point table carries a populated provenance column.

Example

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