A direct method for solving stochastic control problems

Abstract

In this paper a method motivated by completion of squares is used to describe explicit optimal controls for some stochastic control problems that include the linear-quadratic control problem for systems with a general noise process, the linear exponential quadratic Gaussian control problem for systems with Brownian motion, and the control of Brownian motion in the two sphere and the real hyperbolic plane with both finite and infinite time horizons.