{"title":"Autonomous Sparse Mean-CVaR Portfolio Optimization","authors":"Yizun Lin, Yangyu Zhang, Zhao-Rong Lai, Cheng Li","doi":"arxiv-2405.08047","DOIUrl":null,"url":null,"abstract":"The $\\ell_0$-constrained mean-CVaR model poses a significant challenge due to\nits NP-hard nature, typically tackled through combinatorial methods\ncharacterized by high computational demands. From a markedly different\nperspective, we propose an innovative autonomous sparse mean-CVaR portfolio\nmodel, capable of approximating the original $\\ell_0$-constrained mean-CVaR\nmodel with arbitrary accuracy. The core idea is to convert the $\\ell_0$\nconstraint into an indicator function and subsequently handle it through a\ntailed approximation. We then propose a proximal alternating linearized\nminimization algorithm, coupled with a nested fixed-point proximity algorithm\n(both convergent), to iteratively solve the model. Autonomy in sparsity refers\nto retaining a significant portion of assets within the selected asset pool\nduring adjustments in pool size. Consequently, our framework offers a\ntheoretically guaranteed approximation of the $\\ell_0$-constrained mean-CVaR\nmodel, improving computational efficiency while providing a robust asset\nselection scheme.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Portfolio Management","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.08047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 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.