One of the fundamental issues in Control Theory is to design feedback controls. Which is well achieved in the case of linear quadratic control problems. To date, the study of this problem in the stochastic setting is focused much on the natural filtration. In this paper, we utilize the notion of transposition solution to give a sufficient condition for the existence of an optimal feedback control for the stochastic linear quadratic control problems with random coefficients in the general filtration setting, and show it is also necessary for 1-dimensional system.
