Abstract and Applied Analysis
Volume 2011 (2011), Article ID 310910, 20 pages
http://dx.doi.org/10.1155/2011/310910
Research Article

Mean-Variance Hedging and Forward-Backward Stochastic Differential Filtering Equations

Guangchen Wang1,2 and Zhen Wu3

1School of Control Science and Engineering, Shandong University, Jinan 250061, China
2School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China
3School of Mathematics, Shandong University, Jinan 250100, China

Received 22 May 2011; Accepted 28 June 2011

Academic Editor: Gabriel Turinici

Copyright © 2011 Guangchen 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 a mean-variance hedging problem with partial information, where the initial endowment of an agent may be a decision and the contingent claim is a random variable. This problem is explicitly solved by studying a linear-quadratic optimal control problem with non-Markov control systems and partial information. Then, we use the result as well as filtering to solve some examples in stochastic control and finance. Also, we establish backward and forward-backward stochastic differential filtering equations which are different from the classical filtering theory introduced by Liptser and Shiryayev (1977), Xiong (2008), and so forth.