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Optimal Reinsurance and Investment for Stochastic Differential Games with Inflation Influence

??Under inflation influence, this paper investigate a stochasticdifferential game with reinsurance and investment. Insurance company chose a strategyto 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 theinsurance companies and the financial markets, get optimal portfolio strategies. Wheninvesting, 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 differentialgame into unrestricted cases, then application linear-quadratic control theory obtainoptimal reinsurance strategy and investment strategy and optimal market strategy as wellas the closed form expression of efficient frontier are obtained; finally get reinsurancestrategy and optimal investment strategy and optimal market strategy as well as theclosed form expression of efficient frontier for the original stochastic differential game.