Possibilistic mean–variance models and efficient frontiers for portfolio selection problem

Abstract

In this paper, it is assumed that the rates of return on assets can be expressed by possibility distributions rather than probability distributions. We propose two kinds of portfolio selection models based on lower and upper possibilistic means and possibilistic variances, respectively, and introduce the notions of lower and upper possibilistic efficient portfolios. We also present an algorithm which can derive the explicit expression of the possibilistic efficient frontier for the possibilistic mean-variance portfolio selection problem dealing with lower bounds on asset holdings.