Robust and Sparse Portfolio: Optimization Models and Algorithms
The robust and sparse portfolio selection problem is one of the most-popular and -frequently studied problems in the optimization and financial literature. By considering the uncertainty of the parameters, the goal is to construct a sparse portfolio with low volatility and decent returns, subject to...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/24/4925 |
| _version_ | 1797380232720678912 |
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| author | Hongxin Zhao Yilun Jiang Yizhou Yang |
| author_facet | Hongxin Zhao Yilun Jiang Yizhou Yang |
| author_sort | Hongxin Zhao |
| collection | DOAJ |
| description | The robust and sparse portfolio selection problem is one of the most-popular and -frequently studied problems in the optimization and financial literature. By considering the uncertainty of the parameters, the goal is to construct a sparse portfolio with low volatility and decent returns, subject to other investment constraints. In this paper, we propose a new portfolio selection model, which considers the perturbation in the asset return matrix and the parameter uncertainty in the expected asset return. We define three types of stationary points of the penalty problem: the Karush–Kuhn–Tucker point, the strong Karush–Kuhn–Tucker point, and the partial minimizer. We analyze the relationship between these stationary points and the local/global minimizer of the penalty model under mild conditions. We design a penalty alternating-direction method to obtain the solutions. Compared with several existing portfolio models on seven real-world datasets, extensive numerical experiments demonstrate the robustness and effectiveness of our model in generating lower volatility. |
| first_indexed | 2024-03-08T20:34:24Z |
| format | Article |
| id | doaj.art-f78ce2d605574a63a0885030d406ebfa |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T20:34:24Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f78ce2d605574a63a0885030d406ebfa2023-12-22T14:23:19ZengMDPI AGMathematics2227-73902023-12-011124492510.3390/math11244925Robust and Sparse Portfolio: Optimization Models and AlgorithmsHongxin Zhao0Yilun Jiang1Yizhou Yang2School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaDepartment of Economic Management, Shijiazhuang Institute of Railway Technology, Shijiazhuang 050000, ChinaPersonnel Department, Shijiazhuang University, Shijiazhuang 050035, ChinaThe robust and sparse portfolio selection problem is one of the most-popular and -frequently studied problems in the optimization and financial literature. By considering the uncertainty of the parameters, the goal is to construct a sparse portfolio with low volatility and decent returns, subject to other investment constraints. In this paper, we propose a new portfolio selection model, which considers the perturbation in the asset return matrix and the parameter uncertainty in the expected asset return. We define three types of stationary points of the penalty problem: the Karush–Kuhn–Tucker point, the strong Karush–Kuhn–Tucker point, and the partial minimizer. We analyze the relationship between these stationary points and the local/global minimizer of the penalty model under mild conditions. We design a penalty alternating-direction method to obtain the solutions. Compared with several existing portfolio models on seven real-world datasets, extensive numerical experiments demonstrate the robustness and effectiveness of our model in generating lower volatility.https://www.mdpi.com/2227-7390/11/24/4925portfolio optimizationrobustnesssparsityuncertainty setpenalty-alternating-direction method |
| spellingShingle | Hongxin Zhao Yilun Jiang Yizhou Yang Robust and Sparse Portfolio: Optimization Models and Algorithms Mathematics portfolio optimization robustness sparsity uncertainty set penalty-alternating-direction method |
| title | Robust and Sparse Portfolio: Optimization Models and Algorithms |
| title_full | Robust and Sparse Portfolio: Optimization Models and Algorithms |
| title_fullStr | Robust and Sparse Portfolio: Optimization Models and Algorithms |
| title_full_unstemmed | Robust and Sparse Portfolio: Optimization Models and Algorithms |
| title_short | Robust and Sparse Portfolio: Optimization Models and Algorithms |
| title_sort | robust and sparse portfolio optimization models and algorithms |
| topic | portfolio optimization robustness sparsity uncertainty set penalty-alternating-direction method |
| url | https://www.mdpi.com/2227-7390/11/24/4925 |
| work_keys_str_mv | AT hongxinzhao robustandsparseportfoliooptimizationmodelsandalgorithms AT yilunjiang robustandsparseportfoliooptimizationmodelsandalgorithms AT yizhouyang robustandsparseportfoliooptimizationmodelsandalgorithms |