A Krasnoselskii-Mann Proximity Algorithm for Markowitz Portfolios with Adaptive Expected Return Level
Year: 2025
Author: Yizun Lin, Yongxin He, Zhao-Rong Lai
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 1 : pp. 113–138
Abstract
Markowitz’s criterion aims to balance expected return and risk when optimizing the portfolio. The expected return level is usually fixed according to the risk appetite of an investor, then the risk is minimized at this fixed return level. However, the investor may not know which return level is suitable for her/him and the current financial circumstance. It motivates us to find a novel approach that adaptively optimizes this return level and the portfolio at the same time. It not only relieves the trouble of deciding the return level during an investment but also gets more adaptive to the ever-changing financial market than a subjective return level. In order to solve the new model, we propose an exact, convergent, and efficient Krasnoselskii-Mann Proximity Algorithm based on the proximity operator and Krasnoselskii-Mann momentum technique. Extensive experiments show that the proposed method achieves significant improvements over state-of-the-art methods in portfolio optimization. This finding may contribute a new perspective on the relationship between return and risk in portfolio optimization.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1006
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 1 : pp. 113–138
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Markowitz portfolio adaptive expected return ℓ1 regularization Krasnoselskii-Mann algorithm.
Author Details
Yizun Lin Email
Yongxin He Email
Zhao-Rong Lai Email