复合P-G风险下最优投资组合-便宜再保-阈值分红问题  

Optimal Investment Portfolio-Cheap Reinsurance-Threshold Dividend Strategies under Compound Poisson-Geometric Risk Process

作　　者：孙宗岐 杨鹏[2,3] 吴静 杨阳[2] SUN Zongqi;YANG Peng;WU Jing;YANG Yang(School of Medical,Xi'jing University,Xi'an 710123,China;School of Science,Xi'jing University,Xi'an 710123,China;School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710048,China)

机构地区：[1]西京学院医学院,西安710123 [2]西京学院理学院,西安710123 [3]西安交通大学数学与统计学院,西安710048

出　　处：《西南大学学报（自然科学版）》2022年第7期96-105,共10页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(71371152);教育部人文社科一般项目(21XJC910001);陕西省教育厅自然科学专项(20JK0963)。

摘　　要：研究复合Poisson-Geometric风险下带无风险资本的投资组合-比例再保-阈值分红问题,通过使用动态规划原理得到并求解Hamilton-Jacobi-Bellman(HJB)方程,解得最优投资-便宜再保策略与最优分红函数的解析解,最后分析了无风险利率等关键参数对最优策略与最优分红函数的影响,验证了结果的合理性,提出了管理建议.In this paper, the portfolio-proportional reinsurance-threshold dividend problem with risk-free capital under compound Poisson-Geometric risk was studied. The HJB equation was obtained by using the principle of dynamic programming, and the analytic solution of the optimal investment-cheap reinsurance strategy and the optimal dividend function were solved. Finally, the influence of key parameters such as risk-free interest rate on optimal strategy and optimal dividend function was analyzed to verify the rationality of the results and put forward management suggestions.

关 键 词：复合POISSON-GEOMETRIC过程 无风险投资 风险投资 便宜再保 阈值分红 HJB方程 

分 类 号：O211.63[理学—概率论与数理统计]