Recursive moments of the aggregate discounted claims with Erlang inter-occurrence distribution and dependence introduced by a FGM Copula

Abstract

In this paper, we investigate the computation of the moments of the discounted compound renewal aggregate sums when introducing dependence between the inter-occurrence time and the subsequent claim size. We first assume that the inter-occurrence time is following an Erlang distribution and later extend our result to a mixture of Erlangs distribution. The dependence structure between the interoccurrence time and the subsequent claim size is defined by a Farlie- Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we obtain a general formula for any mth order moment. The results are illustrated with applications to premium calculation, moment matching methods, as well as inflation stress scenarios in Solvency Il.