Reserves, mortality and market scenarios, computed in the open.
A vertical actuarial workbench. The reserving and mortality modules compute live in your browser - edit the triangle or the pricing inputs, press the module's compute button, and every figure, factor and error bar recomputes. The market module shows an offline-backtested forecast with its measured error; its 80% interval undercovered the actual path in the recorded backtest (34% coverage) and is not validated for prediction. All math reproduces from public data; every estimate ships with its uncertainty.
Module 1 · P&C reserving · interactive
Chain-ladder reserving computes in this pageCAS-validated on default RAA fixture
Cumulative paid losses, RAA reference dataset (Reinsurance Association of America, Historical Loss Development Study 1991, p.91; the dataset of Mack 1994), $000. Edit any observed cell and recompute: factors, projected development (orange), ultimates, IBNR and Mack standard errors all update in your browser. The same math, run in Python, matches the CAS chainladder-python package (Mack convention) at every displayed decimal.
Observed cells editable; empty cells are unobserved future development.
Module 2 · Life pricing · interactive
Mortality and net premiums computes in this pagereproduces SSA published qx and life expectancies
SSA period life table, 2023 (2026 Trustees Report) - US general population, not insured lives. Net premiums only: no expense loading, no margin, no underwriting classes. Computed life expectancies reproduce SSA's published values (male e₀ 75.79, female e₀ 81.06). The published table ends at age 119 with qx 0.9266 (not 1.0), so a small survival tail beyond 119 is truncated; ages here are capped at 110. Choose inputs and press Compute premiums.
Survival from age 65 by sex (static reference view). Female annuity costs more: lower mortality, longer expected payment stream. Interest rate is an explicit assumption, not a forecast.
Module 3 · Asset-side scenarios · offline results
Kronos-mini market scenarios intervals undercover - see limits
Kronos-mini (4.1M params, MIT code+weights) ran locally on CPU - $0, no API. These are recorded outputs of an offline rolling backtest on SPY daily candles (6 out-of-sample windows, 30-day horizons, 12 sampled paths each, in two separate unseeded runs of 3 windows); the model needs PyTorch and cannot run inside this page, so this module is evidence, not a live calculator. It is a market-price forecaster for the asset side only - not a validated economic scenario generator for regulatory capital.
model 10-90% interval model median actual close (out-of-sample)
Mean abs % error (30d)
4.1%
across 6 out-of-sample windows
80% interval coverage
34%
target is 80% - model is overconfident; per-window 10-93%, weak 12-path estimates
Mean abs error
$30.06
per share, SPY
Compute
$0
local CPU, MIT weights, no credits
Measured, not asserted: the 10-90% band captured the actual path 34% of days overall - per window 93%, 10%, 20% (run A) and 10%, 47%, 23% (run B), two separate unseeded executions joined for display (a prior 8-path run gave 28%). Three weaknesses at once: the model is overconfident, per-window results vary widely, and 12 sampled paths per window make each band a weak empirical estimate. Any capital, reserving or pricing use must recalibrate interval widths first. Sampling used no fixed seed; recorded paths are archived with the build.
Module 4 · Honesty layer
Uncertainty register & human-review boundary
Chain-ladder assumes stable historical development patterns; legal, social-inflation or mix shifts break it. Mack SE is model/parameter risk under Mack assumptions only - not a confidence interval over regime change.
RAA data is reinsurance general liability 1981-1990 (thousands USD). It demonstrates the method, not any current portfolio.
Mortality pricing uses US general-population period mortality (SSA 2023 period table, as used in the 2026 Trustees Report). Insured lives differ. Period tables ignore mortality improvement. Table truncates at age 119 (q=0.9266 for both sexes - a published-table artifact). Net premiums exclude expenses, margins and tax.
Kronos-mini 80% interval coverage on SPY daily measured 34% across 6 out-of-sample windows in the recorded run (28% in a prior 8-path run): the model is overconfident, and with 12-20 sampled paths the interval itself is a weak empirical estimate. Not validated as an economic scenario generator for IFRS 17 / Solvency II.
Interest rates in pricing are flat assumptions, not a yield curve or a forecast.
Nothing here models liability-asset correlation, lapses, catastrophes, reinsurance recoverables, or expenses.
Human-review boundary. All outputs are computational aids for a credentialed actuary, not actuarial advice, pricing decisions, reserve opinions or Statements of Actuarial Opinion. No figure here may be used for regulatory filing, financial reporting, or binding pricing without review and sign-off by a qualified actuary against current data.