A note on compound renewal risk models with dependence

Over the last decade, there have been a significant amount of research works on compound renewal risk models with dependence. These risk models assume a dependence relation between interclaim times and claim amounts. In this paper, we pursue their investigation. We apply change of measure techniques within the compound renewal risk models with dependence to obtain exact expressions for the Gerber-Shiu discounted penalty function. We propose a more general approach than the usual one based on the random walk associated to the risk process as it is presented in the literature. More refined, our method keeps the embedded information in the sequence of claim amounts and interclaim times and enables us to derive an exact expression for the Gerber-Shiu discounted penalty function. Simulation is one of the advantages of change of measure techniques since we can find a new probability measure under which ruin occurs almost surely. In this paper, we investigate the importance sampling method based on change of measure techniques to compute several ruin measures. Numerical illustrations are carried out for specific bivariate distributions of the interclaim time and the claim amount to approximate interesting ruin measures.