A downside risk approach for the portfolio selection problem with fuzzy return

This paper presents a new possibilistic programming approach to the portfolio selection problem. It is based on two issues: the approximation of the rates of return on securities by means of fuzzy numbers of trapezoidal form, for which we use the interval-valued expectation defined by Dubois and Prade, and the perception that down-side risk is a more realistic description of an investor's preferences. We use a data set from the Spanish stock market to illustrate the performance of our method.