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Mathematical Problems in Engineering
Volume 2015, Article ID 892304, 13 pages
http://dx.doi.org/10.1155/2015/892304
Research Article

Maximum Principle for Optimal Control Problems of Forward-Backward Regime-Switching Systems Involving Impulse Controls

School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received 15 April 2014; Accepted 28 August 2014

Academic Editor: Guangchen Wang

Copyright © 2015 Shujun Wang and Zhen Wu. 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

This paper is concerned with optimal control problems of forward-backward Markovian regime-switching systems involving impulse controls. Here the Markov chains are continuous-time and finite-state. We derive the stochastic maximum principle for this kind of systems. Besides the Markov chains, the most distinguishing features of our problem are that the control variables consist of regular and impulsive controls, and that the domain of regular control is not necessarily convex. We obtain the necessary and sufficient conditions for optimal controls. Thereafter, we apply the theoretical results to a financial problem and get the optimal consumption strategies.