The expected discounted penalty function for two classes of risk processes perturbed by diffusion with multiple thresholds

Abstract

In this paper, we consider a perturbed risk model with two independent classes of risks under multiple thresholds in which both of the two inter-claim times have phase-type distributions. We obtain the integro-differential equations with boundary conditions for the expected discounted penalty function. Explicit expressions are derived if the two classes claim amount distributions both belong to the rational family.