A class of possibilistic portfolio selection models and algorithms

Abstract

In this paper, a crisp possibilistic variance and a crisp possibilistic covariance of fuzzy numbers are defined, which is different from the ones introduced by Carlsson and Puller. The possibilistic portfolio selection model is presented on the basis of the possibilistic mean and variance under the assumption that the returns of assets are fuzzy numbers. Especially, Markowitz's probabilistic mean-variance model is replaced a linear programming model when the returns of assets are symmetric fuzzy numbers. The possibilistic efficient frontier can be derived explicitly when short sales are not allowed on all risky assets and a risk-free asset. © Springer-Verlag Berlin Heidelberg 2005.