Over-dispersed Poisson bootstrap

England and Verrall, 1999, Insurance: Mathematics and Economics, on the prediction error of chain ladder. Mack (ASTIN Bulletin, 1993) 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 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. Out comes a histogram of reserves, where the 99.5th percentile is read. Two limits. Residuals are assumed identically distributed, which is false when inflation accelerates. And a triangle sometimes holds only fifty-five points: the bootstrap cannot invent tail that no cell ever observed.