最优再保险及投资组合策略问题  

Optimal Reinsurance and Investment Portfolio Strategy

作　　者：孟辉[1,2] 董纪昌[1] 周县华[2] 

机构地区：[1]中国科学院大学管理学院,北京100190 [2]中央财经大学中国精算研究院,北京100081

出　　处：《数学的实践与认识》2015年第7期79-85,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11271385)

摘　　要：为规避风险的巨大波动,保险公司会将承保的理赔进行分保,即再保险.假定再保险公司采用方差保费准则从保险公司收取保费.应用扩散逼近模型,刻画了保险公司有再保险控制下的资本盈余.另外,保险公司的盈余允许投资到利率、股票等金融市场.通过控制再保险及投资组合策略,研究了最小破产概率.应用动态规划方法(Hamilton-Jacobi-Bellman方程),对最小破产概率、最优再保险及投资组合策略给出了明晰解答,并给出了数值直观分析.To avoid the fluctuation of risk, the insurance company will take reinsurance ar- rangement. Assume that the reinsurance company adopts the variance premium principle. By diffusion approximation, the surplus of the insurance company with reinsurance control is gov- erned by diffusion model. In addition, the insurance company invests its surplus in a risk-free market and stock market. Through controlling reinsurance and investment portfolio strategies, we study the minimal ruin probability. Based on the dynamic programming（Hamilton-Jacobi- Bellman equation）, we give an explicit expression for the minimal ruin probability as well as the optimal reinsurance and investment portfolio strategy, and we also give numerical analysis.

关 键 词：破产概率 方差保费准则 比例再保险 Hamilton—Jacobi—Bellman方程 

分 类 号：F224[经济管理—国民经济] F840