The Discounted Penalty Function with Multi-Layer Dividend Strategy in the Phase-Type Risk Model

Abstract

This paper considers a Sparre Andersen model in which the inter-claim times have a phase-type distribution and the premium rate is a step function depending on the current surplus level. We derive the system of piecewise integro-differential equations for the Gerber-Shiu discounted penalty functions and obtain the closed form expressions of the Gerber-Shiu functions if the claim amount distribution belongs to the rational family. We provide a recursive approach to calculate Gerber-Shiu functions and present an example.