  Motivated by linear-quadratic optimal control problems (LQ problems, for
short) for mean-field stochastic differential equations (SDEs, for short) with
the coefficients containing regime switching governed by a Markov chain, we
consider an LQ problem for an SDE with the coefficients being adapted to a
filtration independent of the Brownian motion driving the control system.
Classical approach of completing the square is applied to the current problem
and obvious shortcomings are indicated. Open-loop and closed-loop solvability
are introduced and characterized.
