Dividend moments for two classes of risk processes with phase-type interclaim times

Abstract

In this paper, we consider the distribution of discounted dividend pay-

ments until ruin under a risk model with two independent classes

of claims in which both of the two interclaim times have phase-

type distributions and a constant dividend barrier. We obtain the

integro-differential equations with boundary conditions for the moment-

generating function of the sum of the discounted dividend payments un-

til ruin. Explicit expressions for arbitrary moments of the discounted

dividend payments are derived if the distribution of the two classes

claim amount both belong to the rational family. Finally, numerical

illustrations are presented to show how the results are applied.

Keywords

• Two classes of risk processes,Dividend payments,Moment-generating function,Dividend barrier,Phase-type distribution

References

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