Before revision:  Key words. time-inconsistency, stochastic linear-quadratic control, uniqueness of equilibrium control, ] forward--backward stochastic differential equation, mean--variance portfolio selection  .
After revision:  Key words. time-inconsistency, stochastic linear-quadratic control, uniqueness of equilibrium control, ] forward--backward stochastic differential equation, mean--variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes .