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Abstract and Applied Analysis
Volume 2014, Article ID 452124, 8 pages
Research Article

Stochastic Maximum Principle for Partial Information Optimal Control Problem of Forward-Backward Systems Involving Classical and Impulse Controls

1School of Science, Dalian Jiaotong University, Dalian 116028, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China

Received 1 January 2014; Revised 28 March 2014; Accepted 29 March 2014; Published 15 April 2014

Academic Editor: Xiaojie Su

Copyright © 2014 Yan Wang 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 partial information classical and impulse controls problem of forward-backward systems driven by Lévy processes, where the control variable consists of two components: the classical stochastic control and the impulse control; the information available to the controller is possibly less than the full information, that is, partial information. We derive a maximum principle to give the sufficient and necessary optimality conditions for the local critical points of the classical and impulse controls problem. As an application, we apply the maximum principle to a portfolio optimization problem with piecewise consumption processes and give its explicit solutions.