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Main Author: Xu, Xin
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2503.06185
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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