A Local Theorem for Ruin Probabilities in the Renewal Risk Model Perturbed by Diffusions

In order to extend the classical risk process to study the possibility of ruin due to various risks, we study the local form of asymptotic estimate for probability in the perturbed renewal risk model which is a more realistic model in insurance and finance. We assume that the relative safety loading condition holds and obtain the asymptotic expression for local ruin probability by using the pure probability method with heavy-tailed claim size, which coincides with that for the corresponding local ruin probability in the renewal risk model. So the influence of the Wiener process can be neglected when the claim size is heavy-tailed.