On the treatment of uncertainty in portfolio selection

Markowitz's classical model, as well as other models derived from it (Tobin, Black, ...), have raised the problem of the analysis and selection of portfolio securities using statistical instruments that assume a regular and efficient market. This is not usually the case. Although some authors have studied this problem using fuzzy formulations, in this paper we propose an alternative for the incorporation of fuzzy numbers to represent the uncertainty of the future return of assets. Subsequently, using the fuzzy return of the portfolio and some measures for risk and for excess return of the portfolio that we define, we will set out the problem of portfolios viewed as a problem of non-linear multiobjective programming with fuzzy parameters that can be solved using a weighted method. Finally, we introduce two examples: the first for the application of our approach and the second for an experimental comparison with the Markowitz model.