Autonomous Sparse Mean-CVaR Portfolio Optimization

Yizun Lin, Yangyu Zhang, Zhao-Rong Lai, Cheng Li
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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.
自主稀疏均值-CVaR 投资组合优化
$\ell_0$约束均值-CVaR模型因其 NP-hard性质而构成重大挑战,通常通过计算要求高的组合方法来解决。我们从一个明显不同的角度提出了一种创新的自主稀疏均值-CVaR组合模型,能够以任意精度逼近原始的 $\ell_0$ 约束均值-CVaR模型。其核心思想是将 $\ell_0$ 约束转换为指标函数,然后通过尾随近似来处理它。然后,我们提出了一种近似交替线性化最小化算法,再加上嵌套定点近似算法(两者都收敛),对模型进行迭代求解。稀疏性自主是指在调整资产池规模时,在选定的资产池中保留相当一部分资产。因此,我们的框架从理论上保证了对 $\ell_0$ 受限均值-CVaR 模型的近似,提高了计算效率,同时提供了一个稳健的资产选择方案。
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