Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation
Haiyang Wang Zhen Wu
In this paper, we study a class of time-inconsistent optimal control problems with random coefficients. By the method of multi-person differential games, a family of parameterized backward stochastic partial differential equations, called the stochastic equilibrium Hamilton-Jacobi-Bellman equation, is derived for the equilibrium value function of this problem. Under appropriate conditions, we obtain the wellposedness of such an equation and construct the time-consistent equilibrium strategy of closed-loop. Besides, we investigate the linear-quadratic problem as a special and important case.
keywords: Time inconsistency equilibrium strategy stochastic partial differential equations equilibrium HJB equation linear-quadratic problem. multi-person differential games

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