Hindawi Publishing Corporation Journal of Applied Mathematics and Decision Sciences Volume 2009, Article ID 609196, 9 pages doi:10.1155/2009/609196

Research Article Discrete Analysis of Portfolio Selection with Optimal Stopping Time
Jianfeng Liang
Department of Risk Management and Insurance, Lingnan (University) College, Sun Yat-Sen University, Guangzhou 510275, China Correspondence should be addressed to Jianfeng Liang, jﬂiang@mail.sysu.edu.cn Received 28 November 2008; Accepted 5 March 2009 Recommended by Lean Yu Most of the investments in practice are carried out without certain horizons. There are many factors to drive investment to a stop. In this paper, we consider a portfolio selection policy with market-related stopping time. Particularly, we assume that the investor exits the market once his wealth reaches a given investment target or falls below a bankruptcy threshold. Our objective is to minimize the expected time when the investment target is obtained, at the same time, we guarantee the probability that bankruptcy happens is no larger than a given level. We formulate the problem as a mix integer linear programming model and make analysis of the model by using a numerical example. Copyright q 2009 Jianfeng Liang. 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.

1. Introduction
Portfolio theory deals with the question of how to ﬁnd an optimal policy to invest among various assets. The mean-variance analysis of Markowitz 1, 2 plays a key role in the theory of portfolio selection, which quantiﬁes the return and the risk in computable terms. The mean-variance model is later extended to the multistage dynamic case. For this and other expected utility-maximization models in dynamic portfolio selection, one is referred to Dumas and Luciano 3 , Elton and Gruber 4 , Li and Ng 5 , Merton 6 ,... [continues]

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