通货膨胀影响下基于随机微分博弈的最优再保险和投资

Optimal Reinsurance and Investment for Stochastic Differential Games with Inflation Influence

本文在通货膨胀影响下,研究了具有再保险和投资的随机微分博弈.保险公司选择一个策略最小化终值财富的方差,而金融市场作为博弈的"虚拟手"选择一个概率测度所代表的经济"环境"最大化保险公司考虑的最小化终值财富的方差.通过保险公司和金融市场之间的这种双重博弈得到最优的投资组合.进行投资时考虑了通货膨胀的影响,通货膨胀的处理方式为:首先考虑通货膨胀对风险资产进行折算,然后再构造财富过程.通过把原先的基于均值-方差准则的随机微分博弈转化为无限制情况,应用线性-二次控制理论得到了无限制情况下最优再保险、投资、市场策略和有效边界的显式解;进而得到了原基于均值-方差准则的随机微分博弈的最优再保险、投资、市场策略和有效边界的显式解.

Under inflation influence,this paper investigate a stochastic differential game with reinsurance and investment.Insurance company chose a strategy to minimizing the variance of the final wealth,and the financial markets as a game ＂virtual hand＂ chosen a probability measure represents the economic ＂environment＂ to maximize the variance of the final wealth.Through this double game between the insurance companies and the financial markets,get optimal portfolio strategies.When investing,we consider inflation,the method of dealing with inflation is：Firstly,the inflation is converted to the risky assets,and then constructs the wealth process.Through change the original based on the mean-variance criteria stochastic differential game into unrestricted cases,then application linear-quadratic control theory obtain optimal reinsurance strategy and investment strategy and optimal market strategy as well as the closed form expression of efficient frontier are obtained;finally get reinsurance strategy and optimal investment strategy and optimal market strategy as well as the closed form expression of efficient frontier for the original stochastic differential game.