Everything on the pricing demo reduces to two equations and one calibrated constant. This page states them formally and shows the calibration test, live, on the public benchmark workloads. The complete validation report (22 cited sources, 63k traces) is available on request.
| the fixed price per unit, the number on the quote | |
| your own unit costs: the empirical distribution fitted from your export, tail blended with the archetype prior at weight 1−Z, Z = n/(n+200) | |
| your average unit cost, its spread, and their ratio (dispersion): all measured, not assumed | |
| your committed weekly volume: bigger books smooth out their own tails, so the middle term shrinks like 1/√V, a diversification credit you earn | |
| the solvency target: the price must cover 99 of 100 simulated weeks before margin | |
| our base margin: fixed, not negotiated per deal | |
| the variance-linked load: riskier books pay more for certainty, in proportion to their own measured dispersion |
Your data sets the mean and the dispersion. Your scale earns the diversification credit.
λ = 0.08 converts your measured dispersion into load: for this book, λ·ĉv = 0.08 × 0.51 = 4.1%. The calibration test: at this price, how much of your premium do we actually keep under each 13-week scenario?
| Scenario | We keep | Losing weeks | Worst week |
|---|---|---|---|
| calm replay · weeks resampled from your own units, no drift | 10.1% of premium | 0 of 13 | $168 |
| hard mix · task-mix drifts week to week, the realistic stress | 11.5% of premium | 1 of 13 | -$138 |
| provider shock · one week at 1.75× cost, gross of the repricing clause | 4.2% of premium | 1 of 13 | -$1,183 |
λ is set so the hard-mix row stays barely positive for high-dispersion books. The calm-week surplus is what pays for the red cells. (A linear λ·ĉv is the v0 rule. The planned upgrade prices load directly off capital consumed under these scenarios.)