On LP Solvable Models for Portfolio Selection

Authors:
Renata Mansini;Włodzimierz Ogryczak;M. Grazia Speranza
Affiliations:
Department of Electronics for Automation, University of Brescia, Via Branze 38, 25123 Brescia, Italy, e-mail: rmansini@ing.unibs.it;Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland, e-mail: w.ogryczak@ia.pw.edu.pl;Department of Quantitative Methods, University of Brescia, C. da S.Chiara 48/B, 25122 Brescia, Italy, e-mail: spreranza@eco.unibs.it
Venue:
Informatica
Year:
2003

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Abstract

The Markowitz model for single period portfolio optimization quantifies the problem by means of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe's work on linear approximation to the mean-variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving Linear Programming (LP) problems. The LP solvability is very important for applications to real-life financial decisions where the constructed portfolios have to meet numerous side constraints and take into account transaction costs. This paper provides a systematic overview of the LP solvable models with a wide discussion of their properties.