RPA pathwise derivative estimation of ruin probabilities

The surplus process of an insurance portfolio is defined as the wealth obtained by the premium payments minus the reimboursements made at the times of claims or accidents. In this paper we address the problem of estimating derivatives of ruin probabilities with respect to the rate of accidents. We study two approaches, one via a regenerative storage process and the other via importance sampling. For both processes we can apply the rare perturbation analysis (RPA) method for sensitivity estimation. We provide computer simulation results.