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Mathematical Problems in Engineering
Volume 2015, Article ID 702802, 12 pages
http://dx.doi.org/10.1155/2015/702802
Research Article

Maximum Principle for Forward-Backward Stochastic Control System Driven by Lévy Process

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China

Received 4 February 2015; Revised 26 April 2015; Accepted 12 May 2015

Academic Editor: Son Nguyen

Copyright © 2015 Xiangrong Wang and Hong Huang. 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 study a stochastic optimal control problem where the controlled system is described by a forward-backward stochastic differential equation driven by Lévy process. In order to get our main result of this paper, the maximum principle, we prove the continuity result depending on parameters about fully coupled forward-backward stochastic differential equations driven by Lévy process. Under some additional convexity conditions, the maximum principle is also proved to be sufficient. Finally, the result is applied to the linear quadratic problem.