ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

doi:10.1016/S0252-9602(10)60140-3

Abstract

Abstract:

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas
for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.

Key words: Markov-dependent risk model, dividend barrier, Gerber-Shiu function, integro-differential equation, Laplace transform

CLC Number:

60J05

LIU Juan, XU Jian-Cheng, HU Yi-Jun. ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER[J].Acta mathematica scientia,Series B, 2010, 30(5): 1481-1491.

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