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.