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Time Inconsistent Stochastic Differential Game: Theory and an Example in Insurance

In this paper, time-inconsistent model was established under stochastic differential game framework. The investment portfolio includes multi-risky assets, whose returns are assumed to be correlated in a time-varying manner and change cyclically. The claim losses of insurance companies and investment are also assumed to be correlated with each other. The Solution to extended HJBI equations results in the portion of retention and an optimal portfolio with equally weighted allocations of risky assets. An optimal control bound is proposed for monitoring and predicting the optimal wealth level. The proposed model is expected to be effective in making decision for investment and reinsurance strategies, controlling and predicting optimal wealth under uncertain environment. Especially, it can be applied easily in the situation of very high dimensional investment portfolio.