A maximização da assimetria na seleção de carteiras eficientes

Abstract

This work deals with investment portfolio selection models that consider higher order moments. It analyzes the structures and support's the mathematical theory in these models,based on a model that considers the first three moments of the multivariate distribution of n risky assets present in a portfolio ,which includes a risk-free asset and allows short sales. We explore the duality of the optimization problems involved, to propose other approaches for the same model and new generalizations. We solve the question of the existence of a solution in these optimization problems, and we delineate the region of duality in the three-moment model, where the optimal portfolios will be efficient, defining conditions so that, given an optimal triple associated with the solution, for any approach of the problem, it is possible to know whether or not it belongs to the duality region and if it is in fact an efficient solution. We also introduce a four-moment model by incorporating kurtosis ,with the presentation of four possible approaches to the three-constraintoptimizationproblemassociatedwiththismodel.Wecomplementall the theory presented, with numerical simulations for the three and four moment models, verifying the effectiveness in the application of both models, and discussing the obtained results.