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运筹学学报 ›› 2012, Vol. 16 ›› Issue (3): 119-131.

• 运筹学 • 上一篇    下一篇

带注资的二维复合泊松模型的最优分红

张帅琪1, 刘国欣2   

  1. 1. 中南大学数学科学与统计学院 2. 河北工业大学理学院
  • 收稿日期:2011-12-29 修回日期:2012-05-18 出版日期:2012-09-15 发布日期:2012-09-18
  • 通讯作者: 张帅琪 E-mail:shuaiqiz@yahoo.com.cn

Optimal dividend payments of the two-dimensional compound Poisson risk model with capital injection

ZHANG Shuaiqi1, LIU Guoxin2   

  1. 1. School of Mathematical Science and Computing Technology, Central South University 2. School of Science, Hebei University of Technology
  • Received:2011-12-29 Revised:2012-05-18 Online:2012-09-15 Published:2012-09-18
  • Contact: ZHANG Shuaiqi E-mail:shuaiqiz@yahoo.com.cn
  • Supported by:

    National Natural Science Foundation of China (No. 10971048)

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1324

被引次数

7

摘要： 研究建立两类理赔关系的二维复合泊松模型的最优分红与注资问题,目标为最大化分红减注资的折现. 该问题由随机控制问题刻画, 通过解相应的哈密尔顿-雅克比-贝尔曼(HJB)方程,得到了最优分红策略,并在指数理赔时明确地解决该问题.

关键词: 最优分红, 注资, 哈密尔顿-雅克比-贝尔曼(HJB)方程, 随机控制, 二维复合泊松模型

Abstract: This paper deals with the optimal dividend payment and  capital injection problem for a two-dimensional compound Poisson risk model which constructs correlation among the two claims. The objective of the corporation is to maximize the discounted dividend payments minus the penalized discounted capital injections. The problem is formulated as a stochastic control problem. By solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we obtain the optimal dividend strategy of the problem. We solve this problem explicitly in the case of exponential claim amount distributions.

Key words: optimal dividends, capital injection, Hamilton-Jacobi-Bellman (HJB) equation, stochastic control, two-dimensional compound Poisson risk model

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