Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 903912, 10 pages
http://dx.doi.org/10.1155/2014/903912
Research Article

On Optimal Control Problem for Backward Stochastic Doubly Systems

Laboratory of Applied Mathematics, University Mouhamed Khider, P.O. Box 145, 07000 Biskra, Algeria

Received 15 December 2013; Accepted 16 January 2014; Published 4 March 2014

Academic Editors: F. Jauberteau and F. Sartoretto

Copyright © 2014 Adel Chala. 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 are going to study an approach of optimal control problems where the state equation is a backward doubly stochastic differential equation, and the set of strict (classical) controls need not be convex and the diffusion coefficient and the generator coefficient depend on the terms control. The main result is necessary conditions as well as a sufficient condition for optimality in the form of a relaxed maximum principle.