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Abstract and Applied Analysis
Volume 2012, Article ID 537376, 29 pages
Research Article

A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints

1Institute for Financial Studies and Institute of Mathematics, Shandong University, Shandong, Jinan 250100, China
2Institute of mathematics, Shandong University, Shandong, Jinan 250100, China

Received 2 October 2012; Accepted 15 November 2012

Academic Editor: Jen-Chih Yao

Copyright © 2012 Shaolin Ji 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.


We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary condition of the stochastic optimal control, that is, stochastic maximum principle, is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.