The phase-type risk model perturbed by diffusion under a threshold dividend strategy

This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the mth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.