The discounted penalty function with multi-layer dividend strategy in the phase-type risk model

Wuyuan Jiang, Zhaojun Yang and Xinping Li

Statistics & Probability Letters, 2012, vol. 82, issue 7, 1358-1366

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.

Keywords: Gerber–Shiu discounted penalty function; Multi-layer dividend strategy; Integro-differential equation; Phase-type distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spl.2012.03.012

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