摘要
金融市场中,保险公司之间存在市场竞争,他们不仅追求自身财富的最大化,同时还关注与竞争对手的财富比较.将模糊厌恶和时滞效应引入到非零和投资与比例再保险策略问题中,研究模糊厌恶水平和时滞效应对互相竞争的保险公司均衡投资和再保险策略的影响.针对经典CramerLundberg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HJB方程,得到了模糊厌恶和时滞效应下基于指数效用的均衡投资与再保险策略以及值函数的显式解.最后结合数值算例仿真分析了模型参数变动对均衡策略的影响.实证结果表明:是否考虑模糊厌恶和时滞信息将大大影响最终的均衡再保险策略和最优投资策略.保险公司对风险的模糊厌恶越高,越多地考虑较早时间的财富值,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 financial market,competitions exist among insurers.The insurers are not only concerned about their own terminal wealth,but also pay attention to the relative performance measured by the difference in their terminal wealth.In this article,we consider a non-zero-sum investment and proportional reinsurance game with ambiguity aversion and delay,and investigate the influence of ambiguity aversion and delay parameters on the optimal investment and reinsurance strategy of competitive insurers.Each insurer’s risk process is described by the classical Cramer-Lundberg model.Each insurer can purchase the proportional reinsurance to mitigate their claim risks;and can invest in one risk-free asset and one risky asset whose price dynamics follows the Black-Scholes model.The main objective of each insurer is to maximize the expected utility of his terminal surplus relative to that of his competitor.Applying the techniques of differential game theory and stochastic optimal control theory,we derive the equilibrium reinsurance and investment strategies explicitly.Finally,we perform some numerical examples to illustrate the influence of model parameters on the equilibrium reinsurance and investment strategies.Numerical simulation results indicate that:Whether the ambiguity aversion and delay information is considered or not will greatly affect the final equilibrium reinsurance strategy and optimal investment strategy.The higher the ambiguity aversion of insurers is,and the more value of wealth at an earlier time is considered,the insurer will be more cautious and rational in their investment;However,the investment strategy of the insurer with the relative performance concern is riskier than that without the concern.
作者
宾宁
朱怀念
BIN Ning;ZHU Huainian(School of Management,Guangdong University of Technology,Guangzhou 510520,China;School of Economics&Commence,Guangdong University of Technology,Guangzhou 510520,China)
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2021年第6期1439-1453,共15页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(71571053,71803029,71940012)
广东省自然科学基金(2018A030313687)。
关键词
模糊厌恶
时滞效应
投资与比例再保险
非零和博弈
NASH均衡
ambiguity aversion
delay effect
investment and proportional reinsurance
non-zero-sum game
Nash equilibrium
作者简介
宾宁(1980-),女,汉,湖北黄石人,广东工业大学管理学院讲师,博士,研究方向:动态博弈理论及应用,保险精算等,E-mail:bbb8087@gdut.edu.cn;通讯作者:朱怀念(1985-),男,汉,安徽蚌埠人,广东工业大学经济与贸易学院副教授,博士,研究方向:动态博弈理论及应用,保险精算等,E-mail:zhuhuainian@gdut.edu.cn。
