数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 791-798.doi: 10.1016/S0252-9602(10)60078-1

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OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

袁海丽, 胡亦钧   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2007-05-16 修回日期:2008-04-30 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

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

OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

 YUAN Hai-Li, HU Yi-Jun   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2007-05-16 Revised:2008-04-30 Online:2010-05-20 Published:2010-05-20
  • Supported by:

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

摘要:

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant
barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.

关键词: Stochastic control, constant barrier, time of ruin, expected discounted dividend payment, moments, Laplace transform of the time of ruin

Abstract:

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant
barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.

Key words: Stochastic control, constant barrier, time of ruin, expected discounted dividend payment, moments, Laplace transform of the time of ruin

中图分类号: 

  • 60J60