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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.06185 |
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| _version_ | 1866909531769929728 |
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| author | Xu, Xin |
| author_facet | Xu, Xin |
| contents | The mean-variance (MV) model is the core of modern portfolio theory. Nevertheless, it suffers from the over-fitting problem due to the estimation errors of model parameters. We consider the $\ell_{1}$ regularized MV model, which adds an $\ell_{1}$ regularization term in the objective to prevent over-fitting and promote sparsity of solutions. By investigating the relationship between sample size and over-fitting, we propose an initial regularization parameter scheme in the $\ell_{1}$ regularized MV model. Then we propose an adaptive parameter tuning strategy to control the amount of short sales. ADMM is a well established algorithm whose performance is affected by the penalty parameter. In this paper, a penalty parameter scheme based on regularized Barzilai-Borwein step size is proposed, and the modified ADMM is used to solve the $\ell_{1}$ regularized MV problem. Numerical results verify the effectiveness of the two types of parameters proposed in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An adaptive ADMM with regularized spectral penalty for sparse portfolio selection Xu, Xin Optimization and Control 90C20, 90C25 The mean-variance (MV) model is the core of modern portfolio theory. Nevertheless, it suffers from the over-fitting problem due to the estimation errors of model parameters. We consider the $\ell_{1}$ regularized MV model, which adds an $\ell_{1}$ regularization term in the objective to prevent over-fitting and promote sparsity of solutions. By investigating the relationship between sample size and over-fitting, we propose an initial regularization parameter scheme in the $\ell_{1}$ regularized MV model. Then we propose an adaptive parameter tuning strategy to control the amount of short sales. ADMM is a well established algorithm whose performance is affected by the penalty parameter. In this paper, a penalty parameter scheme based on regularized Barzilai-Borwein step size is proposed, and the modified ADMM is used to solve the $\ell_{1}$ regularized MV problem. Numerical results verify the effectiveness of the two types of parameters proposed in this paper. |
| title | An adaptive ADMM with regularized spectral penalty for sparse portfolio selection |
| topic | Optimization and Control 90C20, 90C25 |
| url | https://arxiv.org/abs/2503.06185 |