Mack method
Stochastic model that puts a confidence interval around chain ladder without assuming a distribution, by estimating the mean squared error of prediction of the reserve.
Chain ladder returns a number, never an uncertainty. Thomas Mack showed in 1993 that this number follows from just three assumptions, with no probability distribution attached. The expected next cumulative equals the development factor times the current cumulative; accident years are independent; and the variance of the next cumulative is proportional to the current cumulative. From those three he derives the mean squared error of prediction, which adds process risk (future claims are random) to estimation risk (development factors are themselves estimated from few points). The method therefore produces a standard deviation per accident year and for the total reserve, which is what ORSA and Solvency II Pillar 1 demand. It breaks when accident years are not independent, typically after a change in settlement policy or judicial inflation common to every year. The added correlation then appears nowhere in its variance.
Reserve review of a French general liability book as of December 31, 2025, ten accident years. Chain ladder returns a central reserve of 84M EUR. The Mack model returns a standard deviation of 9.2M EUR, a coefficient of variation of 11%, split into 7.4M EUR of process risk and 5.4M EUR of estimation risk. The approximate 90th percentile under a lognormal assumption sits near 96M EUR. That 12M EUR gap is what feeds the reserve risk module; the central reserve does not enter it.
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