带投资的超额损失再保与障碍分红最优化  

Optimal excess of loss reinsurance-barrier dividend strategies with investment

作　　者：孙宗岐 杨鹏 吴静[3] 杨阳 SUN Zongqi;YANG Peng;WU Jing;YANG Yang(School of Medical,Xijing University,Xi’an 710123,Shaanxi Province,P.R.China;School of Statistics,Xi’an University of Finance and Economics,Xi’an 710100,Shaanxi Province,P.R.China;School of Science,Xijing University,Xi’an 710123,Shaanxi Province,P.R.China)

机构地区：[1]西京学院医学院,陕西西安710123 [2]西安财经大学统计学院,陕西西安710100 [3]西京学院理学院,陕西西安710123

出　　处：《深圳大学学报（理工版）》2022年第6期719-724,共6页Journal of Shenzhen University(Science and Engineering)

基　　金：教育部人文社科一般研究资助项目(21XJC910001)。

摘　　要：超额损失再保策略下的最优障碍分红问题迄今鲜有研究.将市场摩擦和终端残值等风险因素与风险资本投资和风险控制策略相结合,研究最优投资-超额损失再保-障碍分红问题.基于动态规划原理建立Hamilton-Jacobi-Bellman方程,通过微分-积分方法求解该方程,获得最优投资-超额损失再保策略和最优障碍分红函数的解析解,并证明最优分红界的存在性和唯一性.The optimal barrier dividend problem under excess of loss reinsurance strategy has rarely been studied so far. We combine the risk factors such as market friction and terminal residual value with risk investment and risk control strategy, and study the resulting optimal investment-excess of loss reinsurance-barrier dividend problem.Based on the dynamic programming principle, we establish the Hamilton-Jacobi-Bellman equation, and obtain the explicit solutions for the optimal investment-excess of loss reinsurance strategy. The optimal dividend function is solved by the differential-integral method. The existence and uniqueness of the optimal dividend boundary is proved.

关 键 词：运筹学与控制论 风险投资 摩擦市场 终端残值 超额损失再保 障碍分红 HAMILTON-JACOBI-BELLMAN方程 

分 类 号：O211.63[理学—概率论与数理统计] F840.32[理学—数学]