Selecting the optimum portfolio using fuzzy compromise programming and Sharpe's single-index model

Different approaches besides the traditional Markowitz's model have been proposed in the literature to analyze portfolio selection problems. Among them, Compromise Programming (CP) is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives. When objectives and constraints are in an imprecise environment Fuzzy CP arises as a suitable solving method. Imprecision will be quantified by means of fuzzy numbers that represent the continuous possibility distributions for fuzzy parameters and hence place a constraint on the possible values the parameters may assume. In this paper a new Fuzzy Compromise Programming approach is proposed based on the obtaining of the minimum fuzzy distance to the fuzzy ideal solution of the portfolio selection problem. Once this fuzzy distance has been obtained the second step consists of finding a crisp decision vector, an optimal portfolio, implying a fuzzy distance to the ideal solution the more accurate as possible to the fuzzy minimum distance previously obtained.