A Stochastic Generalized Network Model and Large-Scale Mean-Variance Algorithm for Portfolio Selection

Abstract

Abstract This paper describes a generalized network framework and an efficient, practical algorithm for large scale mean-variance portfolio selection, based on the nonparametric description of stochastic processes in the frequency domain. A constraint on the variance of uncertain incoming flows to a node in a network model results in a quadratic expression, involving the variance aαd covariance of the distributions of these flows. We show that, when the portfolio variance is decomposed into its frequency components using the Fourier transform, this kind of nonlinear side constraint can be relaxed to produce a set of linear side constraints. Our approach based on this relationship is particularly convenient for large scale problems since no covariance matrix input is required.