均值方差准则下考虑模糊厌恶的随机微分投资与再保险博弈  

Stochastic Differential Investment and Proportional Reinsurance Game under Two Mean-variance Insurers with Ambiguity Aversion

作　　者：宾宁[1] 朱怀念[2] 张成科[2] BIN Ning;ZHU Huai-nian;ZHANG Cheng-ke(School of Management,Guangdong University of Technology,Guangzhou 510520,China;School of Economics&.Commence,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学管理学院,广东广州510520 [2]广东工业大学经济与贸易学院,广东广州510520

出　　处：《系统工程》2022年第4期110-120,共11页Systems Engineering

基　　金：国家自然科学基金资助项目(71571053,71803029,71771058);广东省自然科学基金资助项目(2018A030313687,2017A030313400)。

摘　　要：保险市场中,保险公司之间激烈的市场竞争,使得保险公司不仅追求自身财富最大化,同时还关注与竞争对手之间的财富差距。考虑到金融模型的真实概率测度很难准确估计,将模糊厌恶概念引入到两个保险公司之间的投资再保险博弈问题中,构建了均值方差准则下考虑模糊厌恶的随机微分投资与再保险博弈模型。研究目标是两个保险公司选择均衡投资与再保险策略,在最大化终端时刻相对财富期望值的同时,最小化终端时刻相对财富的方差。针对经典Cramér-Lundberg模型的近似风险扩散过程,运用微分博弈理论和随机最优控制理论,通过求解相应的扩展HJB方程,得到模糊厌恶型保险公司的均衡投资与再保险策略以及值函数的显式解。最后结合数值仿真分析了模糊厌恶系数、对竞争对手财富敏感度等模型参数对保险公司均衡策略影响。研究结果表明:是否考虑模糊厌恶将大大影响最终的均衡再保险策略和投资策略。保险公司对模型不确定性的模糊厌恶越高,在投资行为上就越趋于谨慎理性;而保险公司越看重与对手之间的竞争,则越趋于冒险投资。In the insurance market, competitions exist among insurance companies. The insurance companies not only pursue the maximization of their own wealth, but also pay attention to the wealth comparison with their competitors. Considering the model uncertainty of the financial market, ambiguity aversion is introduced into the non-zero-sum investment and proportional reinsurance game of two insurers. The objective of the insurers is to choose an equilibrium reinsurance-investment strategy so as to maximize the expected relative terminal wealth while minimizing the variance of the relative terminal wealth. Focused on the classical Cramér-Lundberg model, this paper uses the differential game theory and stochastic optimal control theory to solve the corresponding extended HJB equations, obtains the explicit expressions of equilibrium investment and reinsurance strategies and the value functions. A numerical example is given to analyze the sensitivity of equilibrium strategy to model parameters. Research results show that: whether the ambiguity aversion is considered or not, it will greatly influence the final equilibrium reinsurance strategy and equilibrium investment strategy. The higher the ambiguity aversion of insurance companies is, the more cautious and rational insurance companies will be in their investment;however, the more they value competition with their competitors, the more risky insurance companies’ investment will be.

关 键 词：模糊厌恶 均值方差 投资与比例再保险 非零和博弈 

分 类 号：F830[经济管理—金融学]