Hossein Moosaei and Milan Hladík. Minimum norm solution of the Markowitz mean-variance portfolio optimization model. In 38th International Conference on Mathematical Methods in Economics 2020 (MME 2020). Conference Proceedings, pp. 383–388, Mendel University in Brno, 2020.
In finance, Markowitz' model, which is a portfolio optimization model, assists in the selection of the most efficient portfolio by analyzing various possible portfolios of the given securities. This model was considered in many different aspects by researchers. In this paper, we study an extended version of the classical Markowitz' mean-variance portfolio optimization model when this problem has multiple solutions. In this case the natural and in some sense the best choice is finding the solution with minimum norm. We focus on this problem and find the minimum-norm solution of the extended Markowitz's model. To achieve this goal, we characterize the solution set of the model, and by using a standard method and an augmented Lagrangian method we obtain the minimum norm solution of the mentioned problem. The numerical results show that the proposed method is efficient and works well even for large scale problems.
@InProceedings{MooHla2020b,
author = "Hossein Moosaei and Milan Hlad\'{\i}k",
title = "Minimum norm solution of the {Markowitz} mean-variance portfolio optimization model",
editor = "Svatopluk Kapounek and Hana Vr\'{a}nov\'{a}",
booktitle = "38th International Conference on Mathematical Methods in Economics 2020 (MME 2020). Conference Proceedings",
pages = "383-388",
year = "2020",
publisher = "Mendel University in Brno",
isbn = "978-80-7509-734-7",
url = "https://mme2020.mendelu.cz/wcd/w-rek-mme/mme2020_conference_proceedings_final.pdf",
bib2html_dl_pdf = "https://mme2020.mendelu.cz/wcd/w-rek-mme/mme2020_conference_proceedings_final.pdf",
abstract = "In finance, Markowitz' model, which is a portfolio optimization model, assists in the selection of the most efficient portfolio by analyzing various possible portfolios of the given securities. This model was considered in many different aspects by researchers. In this paper, we study an extended version of the classical Markowitz' mean-variance portfolio optimization model when this problem has multiple solutions. In this case the natural and in some sense the best choice is finding the solution with minimum norm. We focus on this problem and find the minimum-norm solution of the extended Markowitz's model. To achieve this goal, we characterize the solution set of the model, and by using a standard method and an augmented Lagrangian method we obtain the minimum norm solution of the mentioned problem. The numerical results show that the proposed method is efficient and works well even for large scale problems.",
keywords = "Markowitz' model; solution set of convex problems; Newton method; augmented Lagrangian method",
}
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