跳-扩散模型下保险公司的博弈问题

摘要

本文研究跳-扩散模型下的具有再保险业务的保险公司非零和博弈问题.假定金融市场可供保险公司投资的金融工具有两种:一种无风险资产(如债券)和一种风险资产(如股票).保险公司可购买比例再保险,同时再保险公司以期望保费原则收取再保险保费,进而建立描述保险公司盈余过程的跳-扩散模型.以两家保险公司终端财富相对差值绩效最大化为目标,建立了两家保险公司的相对绩效最优的HJB方程.通过博弈理论和随机动态规划的方法,证明两家保险公司竞争纳什均衡解的存在性,并给出了纳什均衡耦合系统的隐式解.在特定的保险公司竞争关系下,对两家保险公司之间的最优投资和再保险策略进行分析,分析了模型参数对最优投资策略的影响,并给出相应的经济解释.%In this paper,we combine a jump-diffusion model and the game theory,considering a non-zero reinsurance game between two insurance companies under a jump-diffusion model. We assume that there are one risk-free assets(such as bonds)and one kind of risky assets(such as stock)available for insurance companies to invest. At the same time,this paper considers the optimal reinsurance problem with proportional reinsurance which is assumed to be calculated via the expected premium principle. We establish the Hamilton-Jacobi-Bellman equations under the goal of maximizing the utility of the difference between the two insurance companies' terminal surplus,which is modeled by jump-diffusion risk process. We also prove the existence of Nash equilibrium between the two companies by applying the method of game theory and the stochastic dynamic programming principle,and give a Nash equilibrium strategy. In some special cases, the influences of economic variables on our optimal strategies are demonstrated and some economic explanations are given accordingly.