数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1167-1173.doi: 10.1016/S0252-9602(10)60114-2

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DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

马学敏, 袁海丽, 胡亦钧   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan |430072, China
  • 收稿日期:2007-11-10 修回日期:2008-05-16 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

 MA Xue-Min, YUAN Hai-Li, HU Yi-Jun   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan |430072, China
  • Received:2007-11-10 Revised:2008-05-16 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China

摘要:

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of
exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

关键词: Homogeneous Markov process, ruin probability, deficit, duration of negative surplus, compound Poisson risk model

Abstract:

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of
exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

Key words: Homogeneous Markov process, ruin probability, deficit, duration of negative surplus, compound Poisson risk model

中图分类号: 

  • 60J75