Fuzzy portfolio optimization model under real constraints

This paper discusses a multi-objective portfolio optimization problem for practical portfolio selection in fuzzy environment, in which the return rates and the turnover rates are characterized by fuzzy variables. Based on the possibility theory, fuzzy return and liquidity are quantified by possibilistic mean, and market risk and liquidity risk are measured by lower possibilistic semivariance. Then, two possibilistic mean–semivariance models with real constraints are proposed. To solve the proposed models, a fuzzy multi-objective programming technique is utilized to transform them into corresponding single-objective models and then a genetic algorithm is designed for solution. Finally, a numerical example is given to illustrate the application of our models. Comparative results show that the designed algorithm is effective for solving the proposed models.