Two classes of risk model with di usion 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-dierential equations for the moment-generating function and the rth moment of discounted dividend payments. Explicit expressions for the expectation of discounted dividend payments are derived if the two classes claim amount distributions both belong to the rational family.