Optimal Reinsurance and Dividend Strategies Under the Markov-Modulated Insurance Risk Model

Abstract

In this article, we consider the optimal reinsurance and dividend strategy for an insurer. We model the surplus process of the insurer by the classical compound Poisson risk model modulated by an observable continuous-time Markov chain. The object of the insurer is to select the reinsurance and dividend strategy that maximizes the expected total discounted dividend payments until ruin. We give the definition of viscosity solution in the presence of regime switching. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman equation and a verification theorem is also obtained.

Keywords:

• Compound Poisson model
• Dividend strategy
• HJB equation
• Regime switching
• Reinsurance
• Viscosity solution

Mathematics Subject Classification:

• Primary 93E20
• Secondary 91B70, 60H30

The authors would like to thank the referee for careful reading the paper and the helpful comments and suggestions. J. W. would like to acknowledge the PhD Program Scholarship Fund of ECNU (No. 2010050). H. Y. would like to acknowledge the Research Grants Council of the Hong Kong Special Administrative Region, China (project No. HKU 754008H); R. W. would like to acknowledge the National Natural Science Foundation of China (10971068), National Basic Research Program of China (973 Program) under grant number 2007CB814904, Program for New Century Excellent Talents in University (NCET-09-0356), and the Fundamental Research Funds for the Central Universities.