International Journal of Stochastic Analysis
Volume 2010 (2010), Article ID 329185, 25 pages
doi:10.1155/2010/329185
Research Article

Optimal Control with Partial Information for Stochastic Volterra Equations

Bernt øksendal1,2 and Tusheng Zhang3

1CMA and Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway
2Norwegian School of Economics and Business Administration (NHH), Helleveien 30, 5045 Bergen, Norway
3School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK

Received 26 October 2009; Revised 26 February 2010; Accepted 9 March 2010

Academic Editor: Agnès Sulem

Copyright © 2010 Bernt øksendal and Tusheng Zhang. 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

In the first part of the paper we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus approach, we deduce a general maximum principle for optimal control of general stochastic Volterra equations. The result is applied to solve some stochastic control problem for some stochastic delay equations.