Constraint Method for Possibilistic Mean-variance Portfolio with Transaction Costs and Lending

Portfolio selection is an important issue for researchers and practitioners. Compared with the conventional probabilistic mean-variance method, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. In this paper, the portfolio selection model with transaction costs and lending is proposed by means of possibilistic mean and possibilistic variance under the assumption that the returns of assets are fuzzy numbers. Furthermore, a nonlinear bi-objective programming problem is presented by maximizing the future expected return and minimizing the future risk when the returns of assets are trapezoid fuzzy numbers. By using constraint method, it is converted into a single objective programming problem. Importantly, constraint method concerns better the value ranges of the future expected return and risk for solving single objective programming problem. Finally, a numerical example of the portfolio selection problem is provided to illustrate our proposed effective possibilistic means and variances, and the efficient portfolio frontier with transaction costs and lending can be easily obtained.