A direct approach to linear-quadratic stochastic control
Tyrone E. Duncan
Abstract. A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
Keywords: linear-quadratic Gaussian control, Riccati equation for optimization, stochastic control.
Mathematics Subject Classification: 93E20, 93C05.