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.