Mean-variance portfolio selection with the ordered weighted average

Abstract

Portfolio selection is the theory that studies the pro-cess of selecting the optimal proportion of different assets. The firstapproach was introduced by Harry Markowitz and was based ona mean-variance framework. This paper introduces the orderedweighted average (OWA) in the mean-variance model. The mainidea is to replace the classical mean and variance by the OWA op-erator. By doing so, the new model is able to study different degreesof optimism and pessimism in the analysis being able to develop anapproach that considers the decision makers attitude in the selec-tion process. This paper also suggests a new framework for dealingwith the attitudinal character of the decision maker based on thenumerical values of the available arguments. The main advantageof this method is the ability to adapt to many situations offering amore complete representation of the available data from the mostpessimistic situation to the most optimistic one. An illustrative withfictitious data and a real example are studied.