Affiliation:
1. School of Law, Shanghai University of Finance and Economics, Shanghai 200433, China
2. School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China
Abstract
In this paper, we solve an optimal reinsurance problem in the mathematical finance area. We assume that the surplus process of the insurance company follows a controlled diffusion process and the constant interest rate is involved in the financial model. During the whole optimization period, the company has a choice to buy reinsurance contract and decide the reinsurance retention level. Meanwhile, the bankruptcy at the terminal time is not allowed. The aim of the optimization problem is to minimize the distance between the terminal wealth and a given goal by controlling the reinsurance proportion. Using the stochastic control theory, we derive the Hamilton-Jacobi-Bellman equation for the optimization problem. Via adopting the technique of changing variable as well as the dual transformation, an explicit solution of the value function and the optimal policy are shown. Finally, several numerical examples are shown, from which we find several main factors that affect the optimal reinsurance policy.
Funder
Natural Science Foundation of Chongqing
Talent Initial Funding for Scientific Research of Chongqing Three Gorges University
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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