Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (3): 119-131.

• Original Articles • Previous Articles     Next Articles

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)

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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