带平方根因子过程的保险与再保险公司联合利益的稳健最优投资策略

Robust Optimal Strategies Towards Joint Interests of the Insurer and the Reinsurer with a Square-root Factor Process

由于对模型参数不确定,并且具有模糊厌恶性,大型保险企业的经理正在寻求稳健的最优投资再保险策略.假设风险资产价格满足平方根因子过程.考虑双方的联合利益,把最大化保险公司和再保险公司加权盈余和的期望效用作为目标,导出了稳健的最优投资再保险策略的闭式表达式和相应的值函数,并且给出了验证定理完整的证明.最后,通过一些数值例子分析了模型参数对最优投资策略的敏感性.

A general insurance company which comprises both insurance and reinsurance business lines is considered.The senior management,who is uncertain about the model parameters and ambiguity-averse,is seeking a robust optimal investment-reinsurance strategy.The risky asset price is assumed to satisfy a square root factor process.From the interests of both sides,the maximized goal is the expected utility of the weighted surplus sum of the insurer and reinsurer.On the one hand,the closed-form expressions of the robust optimal strategy and the corresponding value function are derived.On the other hand,the verification theorem is proved completely.Finally,by presenting some numerical examples,model parameters sensitivity to the optimal strategy is shown and explained.