Claim duration — conditions, mortality tables and the months a stop-loss pays

The stop-loss model prices one quote option of a medical stop-loss deal from its census. It has two engines, chosen by data on the model (engine), never by forking code:

A package customises the model for its own book by shipping its own condition set and naming it on its models (conditions, mortality) — the engine stays here, in one place.

The engine, month by month

For every simulation (seeded — the same model gives the same numbers):

1. Onset. Every member, by single age and sex, who is alive and not on claim when the policy year starts, starts at most one claim that year — of a condition group with that group's annual incidence (one draw over the groups), in a uniform month. So a member carries at most one claim in any policy year, and the deductible and the max reimbursement apply per member and policy year, as the terms define them. An age no incidence band covers starts no claim of that group; past the oldest band its rate holds. A lasered claimant — an additional life beside the census, since a laser names no census member — is on claim from month 0 in the group its condition text maps to (the set's keywords; a group id is taken as named; no match → the default group), at the laser's own deductible (never below the specific deductible).
2. On claim. The onset month brings the group's onset cost; each month on claim its monthly cost, times the claimant's cost level (lognormal, mean 1, the group's coefficient of variation), trended per policy year. At each month's end the claimant dies with 1 − (1 − q(x) × excess)^(1/12) — the table's annual rate at the attained age, scaled by the condition's excess mortality, at a constant force within the year — else recovers with the continuation curve's hazard 1 − S(d+1)/S(d), else stays on claim.
3. Cut-off. A claim still running when the contract's incurred period closes is cut off: what it costs afterwards is not covered. (Over several policy years it continues into the next with the deductible reset.)
4. Reimbursement — 12/N. Per claimant and policy year the costs accumulate; above the specific deductible, up to the max reimbursement, the excess is incurred from the piercing month, paid along the completion pattern and reimbursed the lag later. Only what is reimbursed by month N of the year's 12/N basis counts (12/12, 12/15, 12/18); the rest is lost to the run-out and shown as such.

The result has the shape of the default engine's — premium, recoveries, costs, the cumulative result with its P10–P90 band, the first-year loss-ratio spread — so the Result, Cash flows and Summary views and a stored price read either engine the same way. StopLossEngines.Evaluate is the ONE evaluation they all call.

The Duration view

{model}/Duration (only on the duration engine): the expected claimants, the mean months on claim inside the cover, the share of claims ending by recovery, by death and still on claim at the cut-off, the excess lost to the run-out; the on-claim curve per group (no cut-off, averaged over the run's simulated onsets of the census); the groups as a table; every laser with the group it was mapped to and why.

Mortality tables

LossModelling/MortalityTable holds q(x) by age and sex with its provenance (source, publication, basis year, period or cohort, select years, sourced or synthetic). The arithmetic is in Mortality: Q (with an optional improvement scale), Survival (ₙpₓ), CurtateExpectation, CompleteExpectation (curtate + ½), MonthlyQ, Scaled.

Shipped: US population 2024 — SOURCED: the National Center for Health Statistics, United States Life Tables, 2024, National Vital Statistics Reports Vol. 75 No. 5 (Arias, Xu, Tejada-Vera; released 25 August 2026), Table 2 (males) and Table 3 (females), column qx, ages 0–99 as published, unrounded, closing at q = 1 for "100 and over" (https://www.cdc.gov/nchs/data/nvsr/nvsr75/nvsr75-05.pdf; data files at ftp.cdc.gov/pub/Health_Statistics/NCHS/Publications/NVSR/75-05/Table02.xlsx and Table03.xlsx). The tests pin it against the published survivors l(65) and life expectancies e(0), e(65). It is a population table — heavier than an employed, insured group — so as a stop-loss base it is prudent, not fitted.

The demo condition set

US employer health — conditions demo 2026, eight groups: cancer, cardiovascular, end-stage renal disease, transplant and organ failure, neonatal intensive care, neurological and trauma, specialty drugs, other. Demo character only — not a pricing basis.

The condition list follows the categories stop-loss carriers commonly report for high-cost claimants; no carrier's figures are used. Simplifications: no turnover; a member who dies on claim is not replaced (the Population view's members fall by those deaths); members who are not claimants are not exposed to death; claimants already on claim at inception other than the lasered ones are not modelled (the incidence counts onsets); Medicare's secondary-payer switch for renal disease after 30 months is not modelled.