Mean-Variance Portfolio Selection With the Ordered Weighted Average

Portfolio selection is the theory that studies the process of selecting the optimal proportion of different assets. The first approach was introduced by Harry Markowitz and was based on a mean-variance framework. This paper introduces the ordered weighted average (OWA) in the mean-variance model. The main idea is to replace the classical mean and variance by the OWA operator. By doing so, the new model is able to study different degrees of optimism and pessimism in the analysis being able to develop an approach that considers the decision makers attitude in the selection process. This paper also suggests a new framework for dealing with the attitudinal character of the decision maker based on the numerical values of the available arguments. The main advantage of this method is the ability to adapt to many situations offering a more complete representation of the available data from the most pessimistic situation to the most optimistic one. An illustrative with fictitious data and a real example are studied.