Equilibrium of Time-Inconsistent Stochastic Linear--Quadratic Control

In this work, we study equilibrium solutions for a LQ

control problem with state-dependent terms in the objective, which

destroy the time-consisitence of a pre-commited optimal solution.

We get a sufficient condition for equilibrium by a system of

stochastic differential equations. When the coefficients in the

problem are all deterministic, we find an explicit equilibrium

for general LQ control problem. For the mean-variance portfolio

selection in a complete financial market, we also get an explicit

equilibrium with random coefficient of the financial.