In this paper we study a continuous-time stochastic linear quadratic control
problem arising from mathematical finance. We model the asset dynamics with
random market coefficients and portfolio strategies with convex constraints.
Following the convex duality approach, we show that the necessary and
sufficient optimality conditions for both the primal and dual problems can be
written in terms of processes satisfying a system of FBSDEs together with other
conditions. We characterise explicitly the optimal wealth and portfolio
processes as functions of adjoint processes from the dual FBSDEs in a dynamic
fashion and vice versa. We apply the results to solve quadratic risk
minimization problems with cone-constraints and derive the explicit
representations of solutions to the extended stochastic Riccati equations for
such problems.Comment: 22 page
