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Abstract and Applied Analysis
Volume 2014, Article ID 432718, 16 pages
Research Article

An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 26 November 2013; Accepted 2 January 2014; Published 27 February 2014

Academic Editor: Litan Yan

Copyright © 2014 Qingmeng Wei and Xinling Xiao. 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.


This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints. Using Ekeland's variational principle, we obtain one kind of variational inequalities. Then, by dual method, we derive a stochastic maximum principle which gives the necessary conditions for the optimal controls.