Time-inconsistent optimal control problems and the equilibrium hjb equation

Abstract

A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions,a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value function of the problem. Well-posedness such an equation is studied,and time-consistent equilibrium strategies are constructed. As special cases,the linear-quadratic problem and a generalized Merton's portfolio problem are investigated.