A note on discounted compound renewal sums under dependency

The paper considers a renewal risk process in which a given inter-arrival time possibly has an impact on the size of the resulting claim. Under a fairly general dependency structure which contains various well-known examples in the literature as special cases, recursive formulas for the moments of the discounted aggregate claims are derived using the techniques in Léveillé and Garrido (2001b). Simplifications arise in the case of a dependent renewal risk process under ‘Erlang weights’. Numerical examples are given towards the end to illustrate the impact of dependency on the discounted aggregate claims.