通过红利与再保险最大化股东价值的随机控制模型  

A Stochastic Control Model with Maximization of Shareholders Value via Dividend and Reinsurance

作　　者：夏登峰[1] 费为银[1,2] 胡慧敏[1] 

机构地区：[1]安徽工程科技学院应用数理系,安徽芜湖241000 [2]东华大学信息科学与技术学院,上海201620

出　　处：《东华大学学报（自然科学版）》2008年第6期766-770,共5页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金项目(10826098);国家973项目(2007CB814901);教育部博士点基金项目(20060255006);安徽工程科技学院青年基金项目(2007YQ002zd)

摘　　要：主要考虑一类带红利的比例再保险盈余模型.以股东价值最大化为目标,定义值函数为红利的累积折现,在红利折现率为时间的函数时,推导了相应值函数满足的一类Hamilton-Jaccobi-Bellman(HJB)方程,同时对红利和再保险策略的最优控制进行了分析.最优值函数所满足的HJB方程化为了二阶偏微分方程,一般很难求解出其解析解,可以寻求其数值解,得到最优控制.A class of proportional reinsurance surplus model with dividend process is investigated. The insurer＇s objective is to maximize the expected value of future, until ruin time, discounted dividend payments. The discounted rate is fluctuating. The Hamilton-Jaccobi-Bellman （HJB） equation of the insurer＇s value function is first derived. Then, the optimal control on dividend and reinsurance is discussed. The HJB equation of the optimal value function is changed into the partial differential equation of the second order which cannot be generally solved by analitic way. In order to obtain the optimal control, the numerical method is often used to solve the partial differential equation.

关 键 词：变折现率 红利过程 比例再保险 随机控制 HJB方程 

分 类 号：O211.63[理学—概率论与数理统计] F830[理学—数学]