Autonomous Sparse Mean-CVaR Portfolio Optimization

• URL: http://arxiv.org/abs/2405.08047v1
• Date: Mon, 13 May 2024 15:16:22 GMT
• Title: Autonomous Sparse Mean-CVaR Portfolio Optimization
• Authors: Yizun Lin, Yangyu Zhang, Zhao-Rong Lai, Cheng Li,
• Abstract summary: We propose an innovative autonomous sparse mean-CVaR portfolio model, capable of approximating the original model with arbitrary accuracy. We then propose a proximal alternating linearized minimization algorithm, coupled with a nested fixed-point proximity algorithm (both convergent) to iteratively solve the model.
• Score: 6.358973724565783
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The $\ell_0$-constrained mean-CVaR model poses a significant challenge due to its NP-hard nature, typically tackled through combinatorial methods characterized by high computational demands. From a markedly different perspective, we propose an innovative autonomous sparse mean-CVaR portfolio model, capable of approximating the original $\ell_0$-constrained mean-CVaR model with arbitrary accuracy. The core idea is to convert the $\ell_0$ constraint into an indicator function and subsequently handle it through a tailed approximation. We then propose a proximal alternating linearized minimization algorithm, coupled with a nested fixed-point proximity algorithm (both convergent), to iteratively solve the model. Autonomy in sparsity refers to retaining a significant portion of assets within the selected asset pool during adjustments in pool size. Consequently, our framework offers a theoretically guaranteed approximation of the $\ell_0$-constrained mean-CVaR model, improving computational efficiency while providing a robust asset selection scheme.

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