Linear Programming for Portfolio Selection Based on Fuzzy Decision-Making Theory

In this paper, portfolio selection in crisp and fuzzy cases is studied respectively, and corresponding model and algorithms in both case are proposed. In two models, the risk is taken as the sum of the absolute deviation of the risky assets in stead of covariance, the transaction cost is taken as v-shaped function of the difference between the existing and new portfolio. An efficient way is given to transform an optimal problem with non-linear objective function or non-linear constraint into a linear problem, which alleviate the computational difficulty greatly. The investor’s subjective impact is reflected in the model of the fuzzy decision-making environment. Comparison and analysis of the two models is given via a numerical example which has been used in Markowitz’s paper [2].