A Fuzzy Approach to Portfolio Rebalancing with Transaction Costs ⋆ Yong Fang 1 , K.K. Lai 2⋆⋆ , and Shou-Yang Wang 3 1 Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China yfang@amss.ac.cn 2 Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong mskklai@cityu.edu.hk 3 Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China swang@mail.iss.ac.cn Abstract. The fuzzy set is a powerful tool used to describe an uncertain financial environment in which not only the financial markets but also the financial managers’ decisions are subject to vagueness, ambiguity or some other kind of fuzziness. Based on fuzzy decision theory, two portfo- lio rebalancing models with transaction costs are proposed. An example is given to illustrate that the two linear programming models based on fuzzy decisions can be used efficiently to solve portfolio rebalancing prob- lems by using real data from the Shanghai Stock Exchange. 1 Introduction In 1952, Markowitz [8] published his pioneering work which laid the foundation of modern portfolio analysis. It combines probability theory and optimization theory to model the behavior of economic agents under uncertainty. Konno and Yamazika [5] used the absolute deviation risk function, to replace the risk func- tion in Markowitz’s model thus formulated a mean absolute deviation portfolio optimization model. It turns out that the mean absolute deviation model main- tains the nice properties of Markowitz’s model and removes most of the principal difficulties in solving Markowitz’s model. Transaction cost is one of the main sources of concern to portfolio managers. Arnott and Wagner [2] found that ignoring transaction costs would result in an inefficient portfolio. Yoshimoto’s emperical analysis [12] also drew the same conclusion. Due to changes of situation in financial markets and investors’ pref- erences towards risk, most of the applications of portfolio optimization involve a revision of an existing portfolio, i.e., portfolio rebalancing. Usually, expected return and risk are two fundamental factors which investors consider. Sometimes, investors may consider other factors besides the expected ⋆ Supported by NSFC, CAS, City University of Hong Kong and MADIS. ⋆⋆ Corresponding author P.M.A. Sloot et al. (Eds.): ICCS 2003, LNCS 2658, pp. 10-19, 2003.  Springer-Verlag Berlin Heidelberg 2003