Resampling of Pearson residuals from an over-dispersed Poisson model fitted to the triangle, producing the full reserve distribution rather than just its standard deviation.
Mack returns a mean and a standard deviation; regulatory capital, however, is read at a percentile. The ODP bootstrap closes that gap. You fit an over-dispersed Poisson model to the incremental triangle whose central estimates coincide exactly with chain ladder, extract the Pearson residuals, resample them with replacement to build thousands of pseudo-triangles, rerun chain ladder on each, then add to every simulated reserve a process error drawn from a gamma distribution. The output is a histogram of reserves from which the 99.5th percentile is read directly. Two limits matter: residuals are assumed identically distributed, which is false under rising inflation, and a triangle sometimes holds only fifty-five points, so the bootstrap cannot invent tail that no cell ever observed.
Property book of a regional insurer as of June 30, 2026, 10,000 simulations. Central reserve 41.3M EUR, bootstrap mean 41.5M EUR, standard deviation 4.8M EUR, 75th percentile 44.6M EUR, 99.5th percentile 56.1M EUR. The gap between the 99.5th percentile and the mean, 14.6M EUR, is the reserve risk capital charge before diversification.
bootstrap Poisson surdispersée, ODP bootstrap, rééchantillonnage des résidus, bootstrap de provisionnement