Journal of the Operations Research Society of China >

2024 , Vol. 12 >Issue 4: 1022 - 1047

DOI: https://doi.org/10.1007/s40305-024-00551-2

A General Framework for Nonconvex Sparse Mean-CVaR Portfolio Optimization Via ADMM

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  • 1 School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210000, Jiangsu, China;
    2 Center for Mathematical Artificial Intelligence, Department of Mathematics, The Chinese University of Hong Kong, Hong Kong 999077, China

Received date: 2023-09-05

  Revised date: 2024-05-20

  Online published: 2024-12-12

Supported by

This work was supported by the National Natural Science Foundation of China (No. 12001286) and the Project funded by China Postdoctoral Science Foundation (No. 2022M711672).

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Abstract

This paper presents a general framework for addressing sparse portfolio optimization problems using the mean-CVaR (Conditional Value-at-Risk) model and regularization techniques. The framework incorporates a non-negative constraint to prevent the portfolio from being too heavily weighted in certain assets. We propose a specific ADMM (alternating directional multiplier method) for solving themodel and provide a subsequential convergence analysis for theoretical integrity. To demonstrate the effectiveness of our framework, we consider the $\ell$1 and SCAD (smoothly clipped absolute deviation) penalties as notable instances within our unified framework. Additionally, we introduce a novel synthesis of the CVaR-based model with $\ell$1/$\ell$2 regularization. We explore the subproblems of ADMM associated with CVaR and the presented regularization functions, employing the gradient descent method to solve the subproblem related to CVaR and the proximal operator to evaluate the subproblems with respect to penalty functions. Finally, we evaluate the proposed framework through a series of parametric and out-of-sample experiments, which shows that the proposed framework can achieve favorable out-of-sample performance. We also compare the performance of the proposed nonconvex penalties with that of convex ones, highlighting the advantages of nonconvex penalties such as improved sparsity and better risk control.

Key words： Portfolio optimization; Mean-CVaR; Sparse regularization; Alternating direction method of multipliers

Cite this article

Ke-Xin Sun, Zhong-Ming Wu, Neng Wan . A General Framework for Nonconvex Sparse Mean-CVaR Portfolio Optimization Via ADMM[J]. Journal of the Operations Research Society of China, 2024 , 12(4) : 1022 -1047 . DOI: 10.1007/s40305-024-00551-2

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