Decision Support Portfolio rebalancing model with transaction costs based on fuzzy decision theory Yong Fang a , K.K. Lai b,c, * , Shou-Yang Wang a a Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China b Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong c College of Business Administration, Hunan University, Changsha, China Received 3 December 2002; accepted 27 May 2005 Available online 16 August 2005 Abstract The fuzzy set is one of the powerful tools used to describe an uncertain environment. As well as quantifying any potential return and risk, portfolio liquidity is taken into account and a linear programming model for portfolio rebal- ancing with transaction costs is proposed. The level of return that an investor might aspire to, the risk and the liquidity of portfolio are vague in an uncertain financial environment. Considering them as fuzzy numbers, we propose a port- folio rebalancing model with transaction costs based on fuzzy decision theory. An example is given to illustrate the behavior of the proposed model using real data from the Shanghai Stock Exchange. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Portfolio rebalancing; Fuzzy set; Fuzzy decision; Transaction costs 1. Introduction In 1952, Markowitz [14] published his pioneering work which laid the foundation of modern portfolio analysis. MarkowitzÕs model has served as a basis for the development of modern financial theory over the past five decades. However, contrary to its theoretical reputation, it is not used extensively to construct large-scale portfolios. One of the most important reasons for this is the computational difficulty associated with solving a large-scale quadratic programming problem with a dense covariance matrix. Konno and Yamazaki [9] used the absolute deviation risk function to replace the risk function in MarkowitzÕs model 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.05.020 * Corresponding author. Address: Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong. Tel.: +852 27888563; fax: +852 27888560. E-mail address: mskklai@cityu.edu.hk (K.K. Lai). European Journal of Operational Research 175 (2006) 879–893 www.elsevier.com/locate/ejor