Two classes of risk model with diffusion and multiple thresholds: the discounted dividends

Abstract

In this paper, we consider the present value of total dividends until ruin in 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 for the moment-generating function and the $r$th moment of discounted dividend payments. Explicit expressions for the expectation of discounted dividend payments are derived if the two classes claim amountdistributions both belong to the rational family.