Autonomous Sparse Mean-CVaR Portfolio Optimization

TL;DR

This paper introduces an autonomous sparse mean-CVaR portfolio optimization model that approximates the NP-hard original with high accuracy, using a novel algorithm that enhances computational efficiency and asset selection robustness.

Contribution

It proposes a new autonomous sparse mean-CVaR model converting the $\, ext{ extonehalf}\,$ constraint into an indicator function and solving it with a convergent proximal alternating linearized minimization algorithm.

Findings

Provides a theoretically guaranteed approximation of the $\, ext{ extonehalf}\,$-constrained model.

Improves computational efficiency over traditional combinatorial methods.

Maintains significant asset pool during portfolio adjustments.

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.