Compound Poisson Claims Reserving Models: Extensions and Inference

Abstract

We consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.