在CEV模型下带跳的非零和再保险投资博弈  

Non-zero-sum Reinsurance and Investment Game with Jump Under the CEV Model

作　　者：李国柱 马世霞[2] 黄晴 LI Guo-zhu;MA Shi-xia;HUANG Qing(Shanxi Institute of Science and Technology,Jincheng 048000,China;School of Sciences,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]山西科技学院数学教研室,山西晋城048000 [2]河北工业大学理学院,天津300401

出　　处：《数学的实践与认识》2023年第7期29-39,共11页Mathematics in Practice and Theory

基　　金：2022年山西省教育科学规划“十四五”课题:项目名称“新工科”背景下大学数学课程案例数学改革(GH220224)。

摘　　要：研究了两个竟争性保险公司在均值方差准则下的非零和随机微分博弈问题.每个保险公司都能购买再保险,并投资于一个包含无风险资产和风险资产的金融市场,它的风险资产的价格过程由CEV模型描述.特别地,假设每个保险公司的剩余过程遵循跳跃扩散风险模型.应用随机控制方法,推导了均衡投资再保险策略的闭式表达式和相应的价值函数.此外,提供一些数值分析来说明模型参数对均衡投资策略的影响,并得出一些经济解释.In this paper,we investigate a non-zero-sum stochastic differential game between two competitive insurers under the mean-variance criterion.Each insurer is allowed to purchase reinsurance protection and invest in a financial market consisting of one risk-free asset and one risky asset whose price process is described by a constant elasticity of variance(CEV)model.In particular,we assume that each insurer's surplus process follows jumpdiffusion risk model.Applying stochastic control approach,closed-form expressions for the equilibrium investment-reinsurance strategies and corresponding value functions are derived.Finally,we provide some numerical studies to illustrate the influence of model parameters on the equilibrium strategies and draw some economic interpretations.

关 键 词：非零和随机微分博弈 相对绩效 NASH均衡 CEV模型 跳扩散模型 

分 类 号：F840[经济管理—保险] F224.32