Revista de Economía y Negocios

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

Abstract

Hong Mao, Krzysztof Ostaszewski, Zhongkai Wen and Jin Wang

In this paper, we study the retention and investment strategy in a time-inconsistent model for optimal decision problem 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. Extended HJBI equations result in a solution to the portion of retention and an optimal portfolio with equally weighted allocations of risky assets, which is demonstrated first time theoretically. 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. In particular, the model can be applied easily in the case of very high dimensional investment portfolio.