Ornstein-Uhlenbeck模型下保险与再保险的均衡保险投资分析  

The Equilibrium Analysis on the Insurance,Reinsurance and Investment in an Ornstein-Uhlenbeck Model

作　　者：江五元 杨招军 JIANG WUYUAN;YANG ZHAOJUN(Department of Economics and Management,Hunan Institute of Science and Technology,Yueyang 414006,China;Department of Finance,Southern University of Science and Technology,Shenzhen 518055,China;National Center for Applied Mathematics in Shenzhen,Shenzhen 518055,China)

机构地区：[1]湖南理工学院经济与管理学院,岳阳414006 [2]南方科技大学金融系,深圳518055 [3]深圳国家应用数学中心,深圳518055

出　　处：《应用数学学报》2022年第6期905-920,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金重点项目(72031003);湖南省自科基金项目(2020JJ4329);湖南省社科基金项目(18YBA198);广东省哲学社会科学“十三五”规划2019年度项目(GD19CYJ23);深圳市人文社会科学重点研究基地成果资助.

摘　　要：本文构建保险公司和再保险公司的比例再保险与投资组合微分博奔模型,研究两公司基于加权终期财富效用最大化的均衡决策问题.假设保险公司的资本盈余过程为复合Poisson风险跳过程,为降低赔付风险,保险公司可以向再保险公司购买比例再保险。两个公司都可以投资于风险资产满足Ornstein-Uhlenbeck随机模型的金融市场,优化资本管理.在保险公司和再保险公司的绝对风险厌恶指数不随财富数量而变化的假设下,利用博弈论和动态规划原理,得到了两公司的Nash均衡比例再保险和投资组合策略的解析表达式.给出了均衡保险与投资存在的必要条件,对均衡条件下的再保险供需关系进行了分析。We develop a proportional reinsurance and investment differential game model for insurance companies and reinsurance ones and address the optimal decision problem based on the maximization of weighted terminal wealth utility for two companies.We assume that the capital surplus process of insurance companies follows a compound Poisson risk jump process and the insurance companies can purchase proportional reinsurance from reinsurance companies in order to reduce the uncertainty risk arising from random claims.Meanwhile,all the companies can invest in a financial market with a risk-free asset and a risky asset,of which the price follows an Ornstein-Uhlenbeck process for the sake of optimizing capital management.We aim to maximize constant absolute aversion risk utility for both insurance companies and reinsurance companies.We derive the analytical expressions of Nash equilibrium,i.e.the optimal proportional reinsurance and investment strategy for the two companies,by utilizing game theory and the principle of dynamic programming.Finally,we provide an equilibrium analysis on the relationship between reinsurance supply and demand.

关 键 词：Ornstein-Uhlenbeck模型 复合Poisson风险过程 非零和博弈 再保险与投资 

分 类 号：O211.6[理学—概率论与数理统计]