Heston投资模型下的非零和随机微分博弈问题

Non-zero-sum stochastic differential game under the Heston investment model

针对竞争保险公司之间的非零和随机微分博弈问题,本文假设保险公司在购买比例再保险的同时可投资于一个无风险资产和一个具有Heston随机波动率的风险资产。以2家保险公司终端财富相对差值绩效最大化为目标,通过博弈理论和动态规划原理分别得到该博弈在决策者是模糊厌恶和模糊中性2种情形下的纳什均衡再保险投资策略。最后给出一个数值算例阐述参数对纳什均衡策略的影响。

This paper studies the non-zero-sum stochastic differential game between two competing insurance companies.Assume that insurance company can purchase proportional reinsurance and simultaneously invest in a risk-free asset and a risky asset with Heston random volatility in the financial market.Taking the performance maximization of the relative difference of the terminal wealth of two insurance companies as the objective,through the game theory and dynamic programming principle,the Nash equilibrium reinsurance and investment strategies are obtained respectively when the decision makers are ambiguity-averse and ambiguity-neutral.Finally,a numerical example is given to illustrate the influence of parameters on optimal strategy.