  One of the fundamental issues in Control Theory is to design feedback
controls. It is well-known that, the purpose of introducing Riccati equations
in the deterministic case is to provide the desired feedback controls for
linear quadratic control problems. To date, the same problem in the stochastic
setting is only partially well-understood. In this paper, we establish the
equivalence between the existence of optimal feedback controls for the
stochastic linear quadratic control problems with random coefficients and the
solvability of the corresponding backward stochastic Riccati equations in a
suitable sense. We also give a counterexample showing the nonexistence of
feedback controls to a solvable stochastic linear quadratic control problem.
This is a new phenomenon in the stochastic setting, significantly different
from its deterministic counterpart.
