Recursive approaches for multi-layer dividend strategies in a phase-type renewal risk model

In this paper we consider a risk model with two independent classes of insurance risks in the presence of a multi-layer dividend strategy. We assume that both of the claim number processes are renewal processes with phase-type inter-arrival times. By analysing the Markov chains associated with the two given phase-type distributions of the inter-arrival times, algorithmic schemes for the determination of explicit expressions for the Gerber-Shiu expected discounted penalty function, as well as the expected discounted dividend payments are derived, using two different approaches.