On risk models with dependence

Abstract: In this paper we consider the classical and Erlang(2) risk processes when the inter-claim times and claim amounts are dependent. We assume that the dependence structure is defined through a Farlie-Gumbel-Morgenstern (FGM) copula and show that the methods used to derive results in the classical risk model can be modified to derive results in a dependent risk process. We find expressions for the survival probability and the probability of maximum surplus before ruin.