Implementation Notes

Status: Draft, 2026-08-29; citations re-verified against the primary documents 2026-08-30. Built from products/risikolebensversicherung/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 mechanics are sourced — at drafting only through corroboration inherited from a sibling delib research file, and since the 2026-08-30 re-verification from the instruments and wordings themselves: the Bruttobeitrag is guaranteed for the term and the Zahlbeitrag is not R5 R6 REG-R24 REG-R27; the MindZV obliges an insurer to allocate at least 90 % of the Risikoergebnis, which on a term product is essentially the whole technical result R9 REG-R18; § 161 VVG makes the insurer leistungsfrei for an intentional self-inflicted death inside three years, substituting a Rückkaufswert that here is nil or nominal R1 REG-R26; § 169 Abs. 1 VVG confines the surrender-value duty on Kündigung to a contract whose insured event is gewiss, and a term assurance’s is not, so the model carries no cash value at any duration — though two of the three retrieved wordings do provide for one, at a nil-or-nominal amount R2 R3 R8 [S1] [S3] [S4] REG-R28; sex may not enter the premium for contracts concluded from 21 December 2012 R13 REG-R34; and the DeckRV Höchstzinssatz of 1,00 % and Höchstzillmersatz of 25 ‰ of the Summe aller Prämien bound the tariff — both are ceilings the composite adopts as rates, and a retrieved carrier prices at 0,25 % R10 REG-R14 REG-R16 [S3].

Almost no level is sourced, and none is adopted. This model was drafted with direct HTTP egress blocked and the session’s WebSearch budget exhausted before this product was researched, so every level rested on the authoring model’s own knowledge. The citations have since been re-verified against the primary documents — 22 of the 40 entries in sources.md now read Retrieved: yes and 18 still read no. On levels it reached exactly one carrier: [S2]’s published model case gives a Tarifbeitrag, a Zahlbeitrag, an α of 2,41 % and a 0,25 % Rechnungszins, which the standardization table below records as checks and not as inputs. The cost-disclosure duty is owed to the applicant and not to the public R17, so there is still no rate card, and no spread ratio, smoker ratio, commission scale or lapse rate was established for any German carrier [S3]–[S13] [S14] [S16] R18. Every price, charge, margin and behavioural level here is therefore still std with a stated rationale, and the DAV tables — DAV 2008 T, with its NR and R variants — are the property of the Deutsche Aktuarvereinigung, are cited by name and are never shipped R12 REG-R48. Replace the decrement and charge tables with company data before drawing any conclusion from the output.

Run it

python products/risikolebensversicherung/run.py
python products/risikolebensversicherung/run.py 7     # the Einmalbeitrag form
python products/risikolebensversicherung/run.py 8     # the in-force cell, opening at t = 144

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

Projection takes a point_id; Projection[1] is the worked-example anchor cell — entry age 35, male, non-smoker, 300 000 € konstante Versicherungssumme, 25 years’ cover and 25 years’ premium, annual mode, participating. result_cf() returns a DataFrame indexed by the 0-based policy month t with eleven columns; result_cf_annual() sums it into policy years, which is the view the technical notes’ worked example is stated on; and result_pols() publishes the decrement, rate, benefit, premium and reserve side beside the monthly frame.

The time index. t counts policy months from issue and starts at 0: month t runs from time t to time t + 1. proj_len() is the number of projected months, 12 × policy_term, and it is the frame’s exclusive end: result_cf() runs over range(proj_start(), proj_len()), so its last index is proj_len() − 1 and it has 12 × (policy_term − duration_y) rows — three hundred rows t = 0 … 299 on the anchor, 216 rows t = 144 … 359 on the in-force point 8. proj_start() is 12 × duration_y, duration_y being an elapsed count of completed policy years that is already 0-based.

The product is annual and stays annual. duration_mth(t) = t, 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 Nachversicherungsgarantie steps, the § 161 three-year windows, the Beitragszahlungsdauer, the expense inflation, and the whole first-order equivalence — whose G, Gn, v_d and Deckungskapital are bit-identical to the annual-step model this replaced. What the finer grid resolves is 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 model’s own figure.

What the CSVs are keyed on. benefit_schedule.csv, nvg_schedule.csv and lapse_table.csv are keyed on policy_year, the contractual 1-based label, and their values are unchanged by the monthly frame: the readers map through policy_year(t). In model_point_table.csv, duration_y is an elapsed count of years and policy_term and prem_term are counts of years; no column there is a point on the frame’s time axis, so no model-point value moves either. mort_table.csv is keyed on attained age, which is not a time index, and its rates stay annual. No CSV value changed in the move to the monthly grid, and none changed in the earlier move to the 0-based frame.

The model and both its Spaces carry docstrings: model.Projection.doc holds the full mapping between the notes’ actuarial symbols and the cells names, and model.Data.doc says what each input file is and, for the mortality table, what it is not and what a replacement must preserve.

The customer is not billed the premium the contract guarantees

This is the German delta, visible in the frame rather than buried in a parameter. A German Risikolebensversicherung carries two premiums, and a model carrying one cannot represent it R6. The Bruttobeitrag G is struck once, at issue, by first-order equivalence on tariff survivorship — mortality only, no lapse — so it is acyclic with respect to everything behavioural, and it is what the contract guarantees: the maximum the policyholder can ever be required to pay, unchanged for the term R6 REG-R27. The Zahlbeitrag then follows from the surplus mechanic rather than from an assumption — the tariff’s own mortality margin has actuarial value (m/(1+m))·A at issue, and the declared Beitragsverrechnungssatz returns surplus_share of it over the paying term:

G   = ( A + γ·Γ ) / ( (1 − β)·ä − z·k )
    = ( 23 472,374330 + 0,00030 × 6 491 248,23 ) / ( 0,95 × 21,6374941 − 0,025 × 25 )
    = 1 275,411882 €

v_d = min( v_max, decl_scale · surplus_share · (m/(1+m)) · A / (G·ä) )
    = decl_scale · surplus_share · (m/(1+m)) · [ 1 − β − (γ·Γ + z·k·G)/(G·ä) ]
    = 1,00 × 0,90 × 0,5556 × 0,85054952 = 0,42527476

— the surplus share, times the margin fraction of the risk element, times the risk share of the gross premium. So Zahlbeitrag / Bruttobeitrag = 0,574725 on the anchor, reproducing the research file’s frozen std 0.57 from the mechanic rather than by assumption. The model publishes prem_gross (guaranteed), premiums (billed, and the one inside net_cf) and prem_rebate between them.

What the model deliberately does not do here. It does not treat v as a free input, v being an output of the surplus mechanic in the real product; it does not return the Kostenüberschuss alongside the Risikoüberschuss, the MindZV’s übriges Ergebnis limb carrying a different minimum share and no basis for splitting a German term tariff’s expense result having been established R9 — the cost result emerges in net_cf and stays there; and it does not implement § 163 VVG’s Treuhänder adjustment, essentially never used on this product R6 unverified. The lever that matters is decl_scale: setting it to 0 raises premiums to prem_gross at every t — 21 303,65 € against 12 243,75 €, a 74,0 % increase in the bill with no change to any benefit, decrement or guaranteed term, and so with no § 163 procedure, no Treuhänder and no remedy. That is the largest policyholder risk here, and it is a one-Reference change. surplus_form = keine is the § 153-excluded non-participating tariff R5: v_d is zero and the billed premium is the guaranteed one — model point 12, shipped so the zero branch is exercised rather than merely reachable.

The tariff is unisex and the projection is not

Sex may not enter a German premium for contracts concluded from 21 December 2012 R13 REG-R34, while the DAV 2008 T tables the tariff is built on remain sex-distinct R12 REG-R48. Every German term tariff is therefore a blend at a mixing ratio the carrier chooses from its own expected new-business mix — proprietary, unpublished, and one of the largest single sources of unexplained rate spread between German carriers.

mort_rate_tar prices on a 50/50 blend std 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: they pay the same premium to the last bit, beitragsverrechnung_rate() is identical, and their claims_death totals stand at 9 899,20 € against 5 009,05 €. The ratio mort_rate_tar / mort_rate is not 1 + m: it is 2.25 × (unisex blend / own-sex rate), which on the shipped proxy is 1.6875 for a male and 3.375 for a female, the blend being 0.75 × q̃(M). What the model does not do is price on sex, or carry a carrier-specific mixing ratio, none being public; sex_mix_male is a Reference so a user with a real new-business mix can move it in one place, and moving it changes every premium and no claim.

No cash value in the model — and yet a Deckungskapital

§ 169 Abs. 1 VVG confines the surrender-value duty on Kündigung to a policy insuring “ein Risiko …, bei dem der Eintritt der Verpflichtung des Versicherers gewiss ist”, which a term assurance’s is not — read verbatim from the canonical XML R2 REG-R28. So this model carries no account value, no av_pp_at, no surrender cells and no paid-up state, and a lapse is a pure decrement. claims(t, "LAPSE") and claims(t, "MATURITY") are published as zero columns rather than dropped — a non-zero lapse row is what a reader arriving from a US model with cash surrender values will import — and check_no_cash_value() asserts them everywhere.

Read that zero as an approximation of a small number, not as a rule of German law. An earlier draft said § 165’s Beitragsfreistellung right and the insurer-side paid-up conversion “both collapse into the same nil through the minimum-benefit test”. The retrieved wordings do not bear that out. § 165 carries no gewiss limitation, and on a constant sum insured the paid-up right produces a real, small cover: the contract ends only below a paid-up sum of 300 € at Cosmos or 2 500 € at Hannoversche [S3] § 15, [S4] § 13. On Kündigung, the GDV model wording and Hannoversche convert the contract and pay a Rückkaufswert under § 169 — less a Stornoabzug, 60 % of the Deckungskapital at Hannoversche — where that minimum fails; only Cosmos pays nothing at all [S1] § 13 Abs. 8, [S3] § 15 Abs. 10, [S4] § 13. What is uniform is the size, and both wordings say why in the same words: the Kostenverrechnung leaves “keine oder nur geringe Mittel” [S1] § 14 Abs. 4, [S3] § 16 Abs. 4. The cash flow is unaffected either way — a Beitragsfreistellung pays nothing at the time; it converts — so claims_lapse = 0 stands, and changing it would move the worked example and the golden tests, which is a decision for a later pass, not a provenance one.

What is not true is that nothing accumulates, and this is the modelling error the product invites. A level premium charged against a rising death rate overcharges early and undercharges late, and the difference is a Deckungskapital that peaks near the middle of the term and runs off to exactly zero at expiry — 7 553,29 €, 2,52 % of the sum insured, in policy year 15. The reserve takes a policy-year argument and stays an annual construction on the monthly grid, so every figure here is unmoved by the conversion. check_res_roll_fwd() asserts the Thiele recursion with res_pp_at(0) = 0 by the equivalence and res_pp_at(n) = 0 by exhaustion; building on “no Sparanteil, therefore no reserve” fails it.

What the reserve is not. It is a pricing diagnostic: net, not gezillmert, not floored, entering no cash flow, and not a Deckungsrückstellung under HGB § 341f — which requires the prospective method and says nothing about prudent margins, those being DeckRV § 5 Abs. 1’s “Die Ableitung von Rechnungsgrundlagen auf der Basis eines besten Schätzwertes genügt nicht” R21 R10 REG-R54. res_zill_pp_at subtracts the unamortised Zillmer balance and opens at −z·k·G = −797,132426 € — negative from the first day, which is what Zillmerung on a contract with almost no reserve looks like R10. The Nullstellung question — whether a negative individual reserve must be floored for balance-sheet purposes — was not established, and no reserve of any kind enters result_cf().

The § 161 window is three years, and each increment carries its own

§ 161 VVG makes the insurer leistungsfrei where the versicherte Person intentionally takes her own life “vor Ablauf von drei Jahren nach Abschluss des Versicherungsvertrags”, substituting the Rückkaufswert nach § 169 — which on this product is nil or nominal, so the German three-year rule is an exclusion in all but name R1 R2 REG-R26. The per-increment restart is no longer a modelling choice: all three retrieved wordings say “Wenn unsere Leistungspflicht durch eine Änderung des Vertrages erweitert wird oder der Vertrag wiederhergestellt wird, beginnt die Dreijahresfrist bezüglich des geänderten oder wiederhergestellten Teils neu” [S1] § 5 Abs. 3, [S3] § 2 Abs. 4, [S4] § 19 Abs. 3. The model applies it as a benefit switch on death claims only, tranche by tranche:

benefit_paid_pp(t) = S0 · f(t) · Σ_j Δu(y_j) · σ_j(t),
σ_j = 1 − suicide_share  if  duration(t) < y_j + 3

so suicide_factor(t) = benefit_paid_pp(t)/benefit_pp(t) is 0,97 through the first thirty-six months and 1 thereafter on the anchor, and a weighted average strictly between 0,97 and 1 where one tranche is inside its window and another is not — 0,995 through policy years 6 to 8 and 0,9957142857 through policy years 12 to 14 on model point 9, whose Nachversicherungsgarantie steps the sum to 1.2 at policy year 6 (month 60) and 1.4 at policy year 12 (month 132). On the in-force point 8 it is 1 at every projected t.

Both clocks are annual and every window boundary therefore falls on an anniversary, so the monthly grid resolves the switch exactly rather than approximately: duration(t) < 3 is the same statement as t < 36.

What the model does not do. It does not model the mental-illness exception, the ground on which German Selbsttötung claims are actually litigated R23 and not something a best-estimate switch can carry; it does not apply the switch to a lapse or an expiry, both of which pay nothing anyway; and it does not model Nachversicherungsgarantie take-up as a decision — take-up is exogenous, a schedule in nvg_schedule.csv, keine in the base run. The event list, window and caps that were previously unestablished now are: a carrier wording gives nine events, a twelve-month window, 20 % of the original sum insured or 50 000 € per event, five occasions in all and an end above age 50 [S3] § 13. What the model does do with an increment is not exogenous: the clock restarts for it — which all three retrieved wordings provide expressly [S1] [S3] [S4], as does the French statute R1.

Three Versicherungssumme shapes, one mechanic

German tariffs offer konstant, linear fallend and annuitätisch fallend on the same underwriting and Rechnungsgrundlagen. All three are one mechanic — a schedule f(t) on the initial sum — carried as a first-class external input, because a model that hard-codes a constant sum insured cannot represent two of the three shapes the German market sells. The falling shapes price lower mechanically: the equivalence integrates B(t), and nothing is applied as a “discount”. benefit_schedule.csv is term-specific by construction — an amortisation shape is agreed at issue for a stated term — and the annuity shape falls slowly then fast: on point 5 the first year’s fall is 8 407,70 € against 19 236,22 € in the last, the property a linear schedule gets backwards. The nominal rate is a schedule parameter fixed at issue and does not follow a borrower’s loan; no German rate was established, so 3,00 % is std (gap 15). Dynamik — a rising shape — is a different mechanic and is not modelled.

Two lives, one benefit, combined before loading

The verbundene Leben form is one contract on two lives paying once, on the first death — a lives = 2 variant on the same chassis, not a second engine, and off in the base run (model point 10 exercises it). The two lives are combined at table level, before any loading, on an independence assumption std: Q̃ = q̃_A + q̃_B − q̃_A·q̃_B, and the same combination is applied to the two unisex blends before (1 + m)·rf. Combining after loading inflates the cross term; on point 10 the combined rate is 0,0015156941 against a naive sum of 0,0015162642. The assumption understates the true first-death rate for a couple sharing a household, a vehicle and a lifestyle, and no German figure bounds the understatement.

The Über-Kreuz-Versicherung is not in this model, and its absence is deliberate: it is a contracting structure with identical cover, premiums and cash flows, and only the Erbschaftsteuer outcome changes R15 REG-R46. No column, cells or CSV refers to it, and taxation is documented in product-spec.md and computed nowhere.

The last policy year has no lapse

Lapses fall at the end of the month, after the death decrement, and the end of the last month t = proj_len() − 1 is the moment cover expires. A lapse and an expiry are then the same event paying the same nothing, so lapse_rate is 0 through the whole of the final policy year — duration(t) ≥ proj_len_y() − 1, months 288 to 299 on the anchor — and the surviving cohort leaves through pols_maturity. The zero covers the year rather than merely its last month, because that is what the annual-step model this replaced said of it. The table’s own row for policy year n still reads 3 %: the zero is a property of the last policy year, not of the assumption.

No cash flow moves either way, but the closure identity is load-bearing: on the anchor it divides 0,03261764 deaths, 0,53597922 lapses and 0,43140314 expiries, summing to pols_if_init() = 1 exactly with pols_if(300) = 0 — which is what lets result_cf() stop at proj_len() − 1 = 299 with nothing left over. The expiring cohort is the annual-step model’s own figure to the last digit; the split between deaths and lapses moved by 0,00044, which is the one thing interleaving the two decrements monthly genuinely changes.

Inputs are external files

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

products/risikolebensversicherung/
  model_point_table.csv  mort_table.csv  benefit_schedule.csv     <- inputs live here
  nvg_schedule.csv       lapse_table.csv freq_loading_table.csv
  run.py  model.md  product-spec.md  technical-notes.md  sources.md
  RLV_DE_S/                    <- formulas only
    __init__.py  _system.json  Data/__init__.py  Projection/__init__.py

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, and 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 however many policies are projected. The conventions suite counts the reads and asserts the set against tests/de_registry.py.

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

The trade-off: the model is not portable on its own — copy RLV_DE_S/ without the CSVs and it reads fine, then fails on first evaluation. What you gain is that a diff 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. Every file but the model point table carries a per-row provenance column — this library’s second ruling, machine-checked, in the same [S#] / [R#] / [REG-R#] / [std] vocabulary the documents use. model_point_table.csv is the single exemption, a model point being a configuration rather than an assumption.

File	Contents	Provenance
model_point_table.csv	Fourteen model points. Point 1 is the worked-example anchor cell. The rest cover both premium forms, all four Zahlweisen, all three sum shapes, an in-force point opening at t = 144, a Nachversicherungsgarantie with two increments, verbundene Leben, a Risikozuschlag on an impaired smoker, the § 153-excluded tariff, an abgekürzte Beitragszahlungsdauer, and two boundary cells	std; exempt from the provenance rule
mort_table.csv	Second-order annual death rates by table_id, sex, smoker and attained age 18–80	std Gompertz proxy base(sex) × smoker_mult × 1.095^(age−30), base(M) = 0.00040, base(F) = 0.00020, smoker_mult(R) = 2.20. DAV 2008 T / T NR / T R are cited by name and never shipped R12 REG-R48. The three anchors a replacement must preserve: the 50/50 non-smoker blend 0.00030 × 1.095^(x−30), the female-to-male ratio 0.50, and the smoker multiplier 2.20
benefit_schedule.csv	benefit_factor by schedule id and 1-based policy_year, read at t + 1: konstant, linear_fallend ((21 − policy_year)/20, i.e. (20 − t)/20), annuitaet_fallend_3pct	std — the three German shapes are structural [S15]; no schedule parameter was established (gap 15)
nvg_schedule.csv	Cumulative sum_uplift: keine ≡ 1.0, nvg_zwei_erhoehungen stepping to 1.2 at year 6 and 1.4 at year 12	std — the schedule is a mechanics demonstration and take-up is exogenous. Gap 7 is now closed: [S3] § 13 gives a nine-item event list, a twelve-month exercise window, a per-event cap of 20 % of the original sum insured, at most 50 000 €, at most five occasions in all, and an end above age 50. Two 20 % increments are inside those caps; that both are taken is a model assumption no document supports. The CSV is unchanged [S3] [S11] [S17]
lapse_table.csv	Annual lapse by 1-based policy_year, read at policy_year(t), 6 / 4 / 4 / 3 %; spread to the month by lapse_rate_mth	std, argued from structure, not data: nothing is forfeited by lapsing, exit is frictionless because the Versicherungsperiode follows the Zahlweise R8, and the need amortises. The GDV whole-market Stornoquote R18 is deliberately not used (gap 13)
freq_loading_table.csv	Ratenzahlungszuschlag and instalment count by Zahlweise: 1.000 / 1.02 / 1.03 / 1.05	std — a German market convention with no carrier attribution (gap 21). Whether carriers strike it on the Bruttobeitrag or the Zahlbeitrag was not established; this model loads the billed amount

The published identities

Five check_* cells, each a bool over all t with a per-t residual companion check_*_resid(t), and all five called on every model point by the conventions suite. The first is delib’s own ruling and is stated here in one line:

check_net_cf(): result_cf() row t satisfies net_cf = premiums − claims_death − claims_lapse − claims_maturity − expenses − commissions.

It is rebuilt from the frame’s own published columns, and by a different route from net_cf’s own, which subtracts the kind-less claims(t) subtotal. So it crosses the cells-to-frame boundary — a column dropped, renamed or mis-signed on the way into result_cf() fails here — and the claims(t, kind) dispatch, where a benefit kind can exist in the model and not in the subtotal. Which columns are not in it is the other half of publishing it: prem_gross is the guaranteed stream and does not enter, and prem_rebate is the difference between the two premium columns and must not be subtracted again. expenses here excludes commissions — the opposite convention from frlib.TD_FR_S, whose notes fold commission into the expense total. The two libraries’ columns look alike and do not mean the same thing; this identity settles the reading.

Check	Identity
check_net_cf()	On result_cf() row t: net_cf = premiums − claims_death − claims_lapse − claims_maturity − expenses − commissions
check_pols_roll_fwd()	pols_if(t+1) = pols_if(t) − pols_death(t) − pols_lapse(t) − pols_maturity(t), and the three exits sum to pols_if_init()
check_prem_split()	prem_gross_pp(t) = prem_paid_pp(t) + prem_rebate_pp(t), with 0 ≤ prem_rebate_pp < prem_gross_pp where a premium is due and all three zero where none is
check_res_roll_fwd()	The Thiele step (res + Gn·1{t<k})(1+i) = q₁·B + (1−q₁)·res(t+1), plus res_pp_at(0) = 0 and res_pp_at(n) = 0
check_no_cash_value()	claims(t,"LAPSE") = 0 and claims(t,"MATURITY") = 0 at every t

Two further identities are scalar rather than per-period — the first-order equivalence G·ä = A + z·k·G + β·G·ä + γ·Γ and the surplus equivalence v_d·G·ä = decl_scale·surplus_share·(m/(1+m))·A — and are asserted in the product’s test module instead. Forcing a scalar identity into a per-t residual would mean inventing a per-period decomposition the product does not have.

Modules that are off in the base run

Two behavioural 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
Premium-shock lapse	shock_lapse_lambda	0.0	M_shock(t) = 1 + λ_s·max(0, prem_paid_pp(t)/prem_paid_pp(t−12) − 1), reference λ_s = 2.0 std. The ratio is between consecutive renewals, so it reads the annual Zahlbeitrag twelve months back and not the instalment one month back. Inert in the base run because the billed premium is level there; it bites exactly when decl_scale is stressed, which is when it should. A stress that raises the Zahlbeitrag toward the Bruttobeitrag and leaves lapse unchanged is understating itself
Selective lapse	sel_lapse_lambda	0.0, with sel_lapse_ref = 0.25	q₂_eff = q₂·(1 + λ·max(0, w_cum − w_ref)), reference λ = 0.30 std. Healthy lives can re-underwrite into a cheaper contract and impaired lives cannot, so persisters’ mortality drifts up. delib does not model it in the base run — one basis for stayers and leavers — a stated simplification, not an oversight

Both are driven off the premium and the lapse table alone, never off pols_if, so the projection stays acyclic: a pricing quantity struck by equivalence must not depend on a behavioural assumption that depends on the path that depends on the premium. Three further things are described in the sources and not implemented, each because modelling it would add an assumption with no source rather than a mechanic: the Summenzuwachs, verzinsliche Ansammlung and Todesfallbonus surplus forms; the Dynamik and every rider — UZV, BUZ, Beitragsbefreiung, vorgezogene Todesfallleistung, Verlängerungs- and Umtauschoption, vorläufiger Versicherungsschutz; and the Kriegsklausel with its ABC companion, a catastrophe-scenario provision rather than a best-estimate one.

Sign convention

net_cf is income positive — billed premiums in, claims, expenses and commission out — 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. A Solvency II best estimate is Σ v(t)·liability_cf(t) plus a risk margin REG-R1 REG-R2 REG-R6; nothing here discounts a published cash flow — the one place a discount rate appears is the pricing equivalence and the first-order reserve, neither of which is a cash flow.

The shape to expect on the anchor, read on result_cf_annual(), is a first-year strain of −351,88 € — the acquisition cost and initial commission together exceed the first year’s billed premium — thin positive years while the level premium runs ahead of the natural risk premium, and a crossover in policy year 14. Within policy year 1 the monthly frame shows what the annual grid could not: −108,90 € in month 0, where the whole year’s premium is collected against 826,64 € of acquisition cost and commission, then eleven months of about −22 € each. The total is −644,78 € on model point 1 and +4 252,82 € on model point 2, the same cell with sex = F. Neither is a profit measure: the stream is undiscounted, the tariff was struck at 1,00 % on no-lapse survivorship, and no reserve is held against the later years. The difference is the unisex cross-subsidy the law requires, and the model is meant to show that rather than hide it.

Naming

Cells follow lifelib’s basiclife/BasicTerm_S wherever that model has an analogue — model_point, proj_len, age, sum_assured, policy_term, pols_if, pols_death, pols_lapse, pols_maturity, mort_rate, lapse_rate, premiums, claims, expenses, commissions, inflation_factor, net_cf, result_cf — with *_pp for per-policy amounts, claims(t, kind) with an uppercase kind, and pols_if_at(t, timing) for the within-year reads, which is savings/CashValue_SE’s form. The external-CSV layout and Data.input_dir() come from annuallife/TradLife_A. The full symbol mapping lives in the Projection Space docstring. Four cases needed care:

Notes	Cells	Why
Gn, P(t)	prem_net_level_pp / prem_paid_pp	The three “netto”s. prem_net_level_pp is the actuarial Nettoprämie A/ä, a pricing quantity that never becomes a cash flow; prem_paid_pp is the consumer Zahlbeitrag. The Nettotarif is a third, unrelated sense and is not modelled. The bare word Nettobeitrag is never a name here, and prem_net_pp is on the library’s retired-names register
q₁(t), q₂(t)	mort_rate_tar / mort_rate	q₁ prices and enters the premium and the reserve and nothing else; q₂ projects and drives every decrement and claim. Their ratio is 2.25 × (blend / own-sex rate), not 1 + m
B(t)	benefit_pp / benefit_paid_pp	benefit_pp is the contractual Versicherungssumme; what a death claim actually pays differs inside a § 161 window, tranche by tranche, and suicide_factor is the ratio of the two
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

The sister model that shares this chassis is frlib’s TD_FR_S — the French temporaire décès, the same product in another market — and the shared vocabulary is deliberate: pols_if_at, lapse_cum, suicide_factor, benefit_pp, mort_rate_base, prem_freq_load, check_no_cash_value and liability_cf mean the same thing on both. Three differences are named so a reader does not carry one across: the French cotisation is revisable at attained age and the German Bruttobeitrag is level; the French product carries a PTIA acceleration and the German one has no living benefit at all; and expenses includes commission there and excludes it here. Within delib, KLV_DE_S shares the Überschussbeteiligung chassis in a different Überschussverwendung form — surplus credited to a Deckungskapital rather than netted against the premium — and the biometric siblings BU_DE_S and Pflege_DE_S are monthly multi-state models sharing no recursion with this one. issue_date, instalments and policy_id are carried and drive no formula: the notes’ attribute table lists all three, and a silently missing column is worse than an inert one.

Standardizations used

Everything in this table is std. Where an instrument fixes a bound rather than a level — the DeckRV Höchstzinssatz, the Höchstzillmersatz, the MindZV minimum — the bound is cited and the choice to sit at it is the standardization. Where a retrieved document now gives an observed value for a std parameter, the row records it — and the parameter is unchanged. One direct writer’s published model case is not a market, and recalibrating the composite to it would move the worked example and its golden tests. The observations are checks, not inputs.

Parameter	Value	Rationale
mort_table.csv	base(sex) × smoker_mult × 1.095^(age−30)	DAV 2008 T is proprietary and is cited, never shipped R12. The 9,5 % slope is the research file’s own construction with no German source, and on model point 14’s forty-year run it is the single most exposed number in the model
base(M), base(F)	0.00040, 0.00020	Anchored so the 50/50 blend is the research file’s frozen 0.00030 × 1.095^(x−30); the female-to-male ratio 0.50 is the order of magnitude reported for insured lives at these ages unverified
Smoker multiplier	2.20	Mid-point of the two-to-three range reported for insured-lives smoker mortality at working ages unverified; reproduces a premium ratio of 2.007 between points 3 and 1
sicherheitszuschlag_m	1.25	The DAV Richtlinie regulates the procedure for setting the Sicherheitszuschläge, not the level R12 (gap 6); DeckRV § 5 Abs. 1 requires that a loading exist — “Die Ableitung von Rechnungsgrundlagen auf der Basis eines besten Schätzwertes genügt nicht” R10. Calibrated so the derived Zahl/Brutto lands at 0.57; argued range 1.0–1.5. Observed check: a published model case gives Zahl/Brutto = 0.450 [S2], at the bottom of the argued range — i.e. a wider spread than this composite produces
sex_mix_male	0.50	The mechanism is required by law R13; no carrier discloses its own mix
mort_be_factor	1.00	So the shipped proxy is the best estimate, and there is one unsourced mortality level rather than two stacked
surplus_share	0.90	The MindZV minimum allocation from the Risikoergebnis is 90 % R9 REG-R18; modelling the minimum is the conservative choice for the Zahlbeitrag, and it is the only level any instrument fixes
decl_scale	1.00	The insurer declares exactly the minimum. No German declaration for this product was located (gap 1); this is the stress lever
v_max	0.95	A rebate may not exceed the premium. Binds nowhere in the shipped points; it exists so check_prem_split() has a stated domain
zillmer_rate	0.025	The Höchstzillmersatz ceiling R10 REG-R16; the composite assumes a term tariff runs at the cap. Two corrections from retrieved documents. (i) The assumption is close to right for one direct writer: its published model case shows acquisition cost at 2,41 % of the Tarifbeitragssumme [S2]. (ii) But the ceiling is mis-typed as the whole α: DeckRV § 4 caps only the part recovered through Zillmerung, and both the GDV model wording and the carrier AVB spread “die restlichen Abschluss- und Vertriebskosten … über die gesamte Beitragszahlungsdauer” [S1] § 14 Abs. 3, [S3] § 16 Abs. 3. Zillmerung is also optional on this line [S1] fn. 28 (gap 8)
comm_rate_init	0.020 of the Beitragssumme	Splits the α of the ceiling into commission and other acquisition cost. No German commission scale is public
beta_tariff, gamma_rate	0.05 of each Bruttobeitrag; 0.00030 of benefit_pp a year	Correction: German term-life charge levels are not “structurally undisclosed”. § 2 Abs. 1 Nr. 1 VVG-InfoV requires the Abschlusskosten as one total and the other costs as a share of the annual premium, § 2 Abs. 2 requires them in Euro, and § 4 Abs. 2 puts them on the Informationsblatt; both wordings point the customer there [S1] § 14 Abs. 1, [S3] § 16 Abs. 1 R17. What is missing is a published rate card. There is no Effektivkostenquote — § 2 Abs. 1 Nr. 9 confines that duty to a gewiss risk — and no Basisinformationsblatt, the product not being a PRIIP. Observed check: one specimen gives other annual costs of 48,52 € on a 218,52 € annual Tarifbeitrag, i.e. 22,2 %, of which 35,20 € (16,1 %) administration [S2] — far above this composite’s 5 % β, because the specimen’s figure is a euro amount over a small premium, not a percentage loading. Not recalibrated (gap 8)
maint_prem_pct, comm_rate_renew	0.03 and 0.010 of each Zahlbeitrag	Deliberately different from beta_tariff: the gap is the Kostenüberschuss, which is not returned and emerges in net_cf
expense_infl	0.02, on sum-related admin only	The tariff’s γ is level while the modelled one inflates, so the cost result narrows over a long term and eventually reverses — a real feature of a 25-year contract
claim_expense	250 € per death claim	No German figure is public; worth 0,16 € in the anchor’s first year
suicide_share	0.03	No German cause-of-death share was retrieved; stands for “about three per cent of deaths at these ages are suicides”, argued range 0,01–0,05 unverified. The three-year window itself is sourced R1
suicide_years	3	The statutory minimum, extendable by Einzelvereinbarung R1 REG-R26. A Reference so an extended window can be modelled. All three retrieved wordings adopt the statutory three and none extends it [S1] [S3] [S4]
Lapse table	6 % / 4 % / 4 % / 3 % a year, zero through the final policy year	Argued from three structural features (mechanic 17); no German figure supports any of it, argued range 2–8 % in the early durations (gap 13). The final-year zero is a property of the last policy year and lives in the formula, not the table. The annual rate is spread to the month at 1 − (1 − w)^(1/12) std: no German instrument states a conversion convention for any decrement, and what is not optional is that twelve of the monthly rates compound back to the year’s
prem_freq_load	1.000 / 1.02 / 1.03 / 1.05	A market convention with no carrier attribution (gap 21), applied to the billed amount so the split identity holds at every frequency
Benefit schedules	(21 − policy_year)/20, i.e. (20 − duration(t))/20, stepping on the anniversary; a 3,00 % thirty-year annuity balance	The three shapes are structural; no schedule parameter was established (gap 15)
NVG schedule	1.2 at year 6, 1.4 at year 12	Take-up is exogenous. Gap 7 is closed and the schedule is not consistent with the one wording that fills it: [S3] § 13 caps each event at 20 % of the original sum insured, at most 50 000 €, allows at most five occasions and ends the right above age 50, all within a twelve-month window of a listed event. Two increases of +20 % each is within that; but a cumulative 1.4 by year 12 assumes two qualifying events and full take-up, which no document supports. The schedule is unchanged — it is a mechanics demonstration, off in the base run — and the carrier’s caps are now on the record beside it
lives = 2 combination	q_A + q_B − q_A·q_B, before loading	An independence assumption that understates the true first-death rate for a couple; no German figure bounds it (gap 15)
rating_factor	1.00 standard, 1.75 on point 11	A Risikozuschlag is a mortality loading on both orders, not a price loading — which is why the Zahl/Brutto ratio moves by less than half a point across it. No German or French Risikozuschlag scale is public
premium_form = einmal	Model point 7	A std construction exercising the premium engine at k = 1. No German standalone RLV in the corpus is written on it; the out-of-scope Restschuldversicherung is, and it is a different product sold a different way
Timing conventions	A premium instalment on the Zahlweise’s own cycle and the month’s expenses at the beginning of the month, claims and lapses at the end, acquisition cost at issue only where duration_y = 0	The approximation this row used to record is gone. On the annual grid the model booked exits at anniversaries and said so, and the note recorded that the approximation was larger than first assumed: § 168 Abs. 1 with § 12 VVG gives termination at the end of the Versicherungsperiode, but both retrieved carriers allow it “jederzeit zum Ende des laufenden Monats” whatever the Zahlweise [S3] § 15 Abs. 9, [S4] § 13 Abs. 1. The monthly grid expresses exactly that. What remains std is the conversion of the annual rates to the month and the placing of claims at the end of the month
shock_lapse_lambda, sel_lapse_lambda	0.0 (references 2.0 and 0.30)	Both modules off, so the base run reproduces the worked example
roll_fwd_tol, val_tol	1e-10, 1e-9	Tolerances scaled by pols_if_init() and sum_assured() respectively
The fourteen model points	—	The anchor is the research file’s representative composite; the rest are chosen to exercise the mechanics, not to describe a market

The only quantities not standardizations are the structural rules: the guaranteed Bruttobeitrag and non-guaranteed Zahlbeitrag R6 [S3] [S5], the MindZV’s 90 % minimum from the Risikoergebnis, now citable as § 7 MindZV R9, the three-year § 161 window R1 and its restart for each increment [S1] [S3] [S4], the unisex rule R13, the DeckRV ceilings of 1,00 % and 25 ‰ R10, and the absence of a premium-tax line, VersStG 2021 § 4 Abs. 1 Nr. 5 Buchst. a R16.

One item has moved off that list. “The absence of any surrender, paid-up or maturity value” was carried here as a structural rule. It is not one. No § 169 Abs. 1 duty attaches on Kündigung — that much is verified R2 — but § 165’s paid-up right is live on a constant sum insured, and two of the three retrieved wordings pay a Rückkaufswert where the paid-up sum fails a contractual minimum [S1] [S4]. The amount is nil or nominal in every one of them, so claims_lapse = 0 and claims_maturity = 0 remain right as best-estimate approximations — but they belong in the table above, as standardizations, not here.

Tests

tests/test_risikolebensversicherung_de.py asserts all twenty-five rows of the notes’ annual worked example — off result_cf_annual(), keyed on the 1-based policy_year — to the cent and pols_if to six decimals, the twelve months of policy year 1 on the monthly frame beside them, that the annual view regroups the monthly frame rather than reprojecting it, the frame’s own shape (list(result_cf().index) == list(range(300)) on the anchor and range(144, 360) on the in-force point 8), the totals at full precision, the Bruttobeitrag 1 275,411882 € and the Beitragsverrechnungssatz 0,42527476 reached two independent ways, the notes’ three rebuilds and three closure identities, the decl_scale = 0 and Einmalbeitrag variant tables, the five check_* identities with their residuals, and one test per listed modeling pitfall — the three “netto”s in the order the model produces them, two premium streams rather than one, the Zahlbeitrag not guaranteed, no Rückkaufswert, a Deckungskapital that exists, sex never reaching the price, the Sicherheitszuschlag never reaching the projection, the § 161 switch confined to three years and to death claims, the clock restarting per increment, the Ratenzahlungszuschlag applied once, premium cessation not double-counted, the premium stopping at the Beitragszahlungsdauer, the three sum shapes, two lives combined before loading, the Kostenüberschuss not returned, the Stornoquote not used, rating_factor never scaling the benefit, and the Über-Kreuz-Versicherung not a product.

The house style — two Spaces, the external-CSV layout, the read-once Data, the shared vocabulary, the retired names, the 0-based frame ending at proj_len() − 1, the round trip and both of delib’s own rulings — is asserted for every model by tests/test_model_conventions_de.py, which also owns the library’s single model-point sweep.

python -m pytest tests -q