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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 216891, 17 pages
http://dx.doi.org/10.1155/2012/216891
Research Article

Multi-Period Mean-Variance Portfolio Selection with Uncertain Time Horizon When Returns Are Serially Correlated

1School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China
2Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China
3Lingnan (University) College/Business School, Sun Yat-Sen University, Guangzhou 510275, China

Received 27 November 2011; Accepted 8 February 2012

Academic Editor: Yun-Gang Liu

Copyright © 2012 Ling Zhang and Zhongfei Li. 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

We study a multi-period mean-variance portfolio selection problem with an uncertain time horizon and serial correlations. Firstly, we embed the nonseparable multi-period optimization problem into a separable quadratic optimization problem with uncertain exit time by employing the embedding technique of Li and Ng (2000). Then we convert the later into an optimization problem with deterministic exit time. Finally, using the dynamic programming approach, we explicitly derive the optimal strategy and the efficient frontier for the dynamic mean-variance optimization problem. A numerical example with AR(1) return process is also presented, which shows that both the uncertainty of exit time and the serial correlations of returns have significant impacts on the optimal strategy and the efficient frontier.