Journal of Applied Mathematics
Volume 2012 (2012), Article ID 835319, 22 pages
http://dx.doi.org/10.1155/2012/835319
Research Article

Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

Li Chen,1 Zhen Wu,2 and Zhiyong Yu3

1Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
2School of Mathematics, Shandong University, Jinan 250100, China
3School of Economics, Shandong University, Jinan 250100, China

Received 25 May 2012; Accepted 30 July 2012

Academic Editor: Ying Hu

Copyright © 2012 Li Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.