Optimal Control of Constrained Stochastic Linear-Quadratic Model with Applications
Provides an explicit solution for a class of constrained LQ problems, enabling efficient computation for applications like portfolio selection.
This paper solves a constrained stochastic LQ optimal control problem by deriving an explicit piece-wise affine optimal control policy via the state separation theorem, computable by solving two Riccati equations. The method is applied to dynamic mean-variance portfolio selection.
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop the explicit solution for this class of problem. The revealed optimal control policy is a piece-wise affine function of system state. This control policy can be computed efficiently by solving two Riccati equations off-line. Under some mild conditions, the stationary optimal control policy can be also derived for this class of problem with infinite horizon. This result can be used to solve the constrained dynamic mean-variance portfolio selection problem. Examples shed light on the solution procedure of implementing our method.