stochastic reserving (Mack, bootstrap)

The chain ladder hands you one number: the reserve is 5 million. But that single point answer hides the question every executive really wants answered — how wrong could we be? Is the true cost almost certainly between 4.8 and 5.2 million, or could it plausibly be 3 or 8? Stochastic reserving methods attach a probability distribution to the reserve estimate, turning a single best guess into a range with a measure of uncertainty around it.

Precisely, stochastic reserving methods estimate not just the expected reserve but its variability — typically a standard error and a full predictive distribution. Mack's method is a distribution-free approach that derives formulas for the standard error of the chain-ladder estimate directly from the triangle, under explicit assumptions about how development factors behave. The bootstrap is a simulation approach: it repeatedly resamples the historical residuals of the chain-ladder fit to generate thousands of plausible alternative triangles, runs the chain ladder on each, and reads the spread of the resulting ultimates as the reserve distribution. For example, a point reserve of 5 million might come with a Mack standard error of 0.6 million, implying a rough 1-in-200 (99.5th percentile) reserve nearer 6.5 million — the kind of figure capital regimes care about.

Stochastic reserving matters because solvency frameworks (Solvency II, risk-based capital, IFRS 17 risk adjustment) demand a quantified view of reserve uncertainty, not just a midpoint. It also forces honesty: the range is usually much wider than non-actuaries expect. Two important caveats: these methods quantify only the uncertainty captured by the model's assumptions — they say nothing about model risk (the chance the chain ladder itself is the wrong model) or about structural changes the data has not yet revealed. A narrow stochastic range is therefore not a guarantee of accuracy; it can simply mean the model is confidently wrong.