Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model

Abstract

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.

Keywords

• two-classes of claim
• renewal risk processes
• multi-layer dividend strategy
• phase-type distribution
• Gerber–Shiu function
• expected discounted dividend payments