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 and some properties
of 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.Comment: 51 page
