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Mathematical Problems in Engineering
Volume 2013, Article ID 613159, 7 pages
http://dx.doi.org/10.1155/2013/613159
Research Article

Optimality Conditions for Optimal Control of Jump-Diffusion SDEs with Correlated Observations Noises

School of Mathematics and Statistics, Shandong University, Weihai 264209, China

Received 25 January 2013; Accepted 5 March 2013

Academic Editor: Guangchen Wang

Copyright © 2013 Hua 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.

Abstract

This paper is concerned with necessary and sufficient optimality conditions for optimal control of jump-diffusion stochastic differential equations. Compared with the existing literature, there are two distinguishing features: one is that the states are driven by Brownian motions and Poisson random measure; the other one is that the states and the observations are correlated. We derive a necessary and a sufficient conditions in the form of maximum principle when control domain is convex. A linear-quadratic example is worked out to illustrate the applications of the foregoing optimality conditions.