An interval portfolio selection problem based on regret function

Different approaches, besides the traditional Markowitz's model, have been proposed in the literature to analyze portfolio selection problems. Among them we can cite the possibilistic portfolio models, which treat the expected return rates of the securities as fuzzy or possibilistic variables, instead of random variables. Such models, which are based on possibilistic mathematical programming, describe the uncertainty of the real world as ambiguity and vagueness, rather than stochasticity. Actually, another way to treat the uncertainty in decision making problems consists of assuming that the data are not well defined, but are able to vary in given intervals. Interval analysis is thus appropriate to handle the imprecise input data. In this paper we consider a portfolio selection problem in which the prices of the securities are treated as interval variables. In order to deal with such an interval portfolio problem, we propose the adoption of a minimax regret approach based on a regret function.