A class of fuzzy portfolio selection problems

There are many non-probabilistic factors that affect the financial markets. Fuzzy number is a powerful tool used to describe an uncertain environment with vagueness and ambiguity. This paper discusses portfolio selection problem when returns of assets are fuzzy numbers. The Markowitz's mean-variance model, quadratic programming, are replaced by linear programming models based on the lower and upper possibilistic means and possibilistic variances when returns of assets are fuzzy numbers with linear or segmented linear membership functions. Using some related algorithms for solving linear programming problem, the lower and upper possibilistic efficient portfolios are easily obtained.