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

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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. 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 Juan1, 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:

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:

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

中图分类号: 

  • 60J05