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

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

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1481-1491.doi: 10.1016/S0252-9602(10)60140-3

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

刘娟^{1, 2}, 徐建成¹, 胡亦钧²

1. College of Mathematics and Statistics, |Hubei Normal University, Huangshi 435002;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072

收稿日期:2008-10-24 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
This work was supported in part by Hubei Normal University Post-graduate Foundation (2007D59 and 2007D60), the Science and Technology foundation of Hubei (D20092207), and the National Natural Science Foundation of China (10671149).

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

LIU Juan^{1, 2}, XU Jian-Cheng¹, HU Yi-Jun²

Received:2008-10-24 Online:2010-09-20 Published:2010-09-20
Supported by:
This work was supported in part by Hubei Normal University Post-graduate Foundation (2007D59 and 2007D60), the Science and Technology foundation of Hubei (D20092207), and the National Natural Science Foundation of China (10671149).

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

60J05

刘娟, 徐建成, 胡亦钧. ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER[J]. 数学物理学报(英文版), 2010, 30(5): 1481-1491.

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

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

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