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Multi-period mean–variance portfolio optimization with capital injections

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  • Shi, Longyu
  • Wang, Yunyun
  • Li, Wenyue
  • Zhang, Zhimin

Abstract

In this study, we explore the portfolio optimization problem where the investors initially allocate portions of their capital across a large asset pool, followed by gradual capital injections over the subsequent periods. We introduce a multi-period mean–variance model with capital injections to develop a sparse long-term investment strategy within this framework. This model adopts the fused Lasso technique, integrating two ℓ1 penalty terms designed to lower both holding and trading costs. We utilize a two-block alternating direction method of multipliers algorithm to solve this complex, non-smooth optimization problem involving multiple variables. A thorough analysis of the convergence of the algorithm is provided. In addition, we empirically validate the efficacy of our model using two real datasets, demonstrating its practical applicability and effectiveness in real-world scenarios.

Suggested Citation

  • Shi, Longyu & Wang, Yunyun & Li, Wenyue & Zhang, Zhimin, 2025. "Multi-period mean–variance portfolio optimization with capital injections," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 400-412.
    • Handle: RePEc:eee:matcom:v:233:y:2025:i:c:p:400-412
    DOI: 10.1016/j.matcom.2025.02.006
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    References listed on IDEAS

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    1. Zhifeng Dai & Jie Kang, 2022. "Some new efficient mean–variance portfolio selection models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4784-4796, October.
    2. Hongxin Zhao & Lingchen Kong & Hou-Duo Qi, 2021. "Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm regularization," Computational Optimization and Applications, Springer, vol. 80(3), pages 853-881, December.
    3. Ye, Gui-Bo & Xie, Xiaohui, 2011. "Split Bregman method for large scale fused Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1552-1569, April.
    4. Michael Ho & Zheng Sun & Jack Xin, 2015. "Weighted Elastic Net Penalized Mean-Variance Portfolio Design and Computation," Papers 1502.01658, arXiv.org, revised Oct 2015.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    7. Yongjae Lee & Min Jeong Kim & Jang Ho Kim & Ju Ri Jang & Woo Chang Kim, 2020. "Sparse and robust portfolio selection via semi-definite relaxation," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(5), pages 687-699, May.
    8. Corsaro, Stefania & De Simone, Valentina & Marino, Zelda, 2021. "Split Bregman iteration for multi-period mean variance portfolio optimization," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    9. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    10. Jingnan Chen & Gengling Dai & Ning Zhang, 2020. "An application of sparse-group lasso regularization to equity portfolio optimization and sector selection," Annals of Operations Research, Springer, vol. 284(1), pages 243-262, January.
    11. Kirkby, J. Lars & Mitra, Sovan & Nguyen, Duy, 2020. "An analysis of dollar cost averaging and market timing investment strategies," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1168-1186.
    12. Kremer, Philipp J. & Lee, Sangkyun & Bogdan, Małgorzata & Paterlini, Sandra, 2020. "Sparse portfolio selection via the sorted ℓ1-Norm," Journal of Banking & Finance, Elsevier, vol. 110(C).
    13. Stefania Corsaro & Valentina De Simone & Zelda Marino & Francesca Perla, 2020. "$$l_1$$ l 1 -Regularization for multi-period portfolio selection," Annals of Operations Research, Springer, vol. 294(1), pages 75-86, November.
    14. Stefania Corsaro & Valentina De Simone & Zelda Marino & Salvatore Scognamiglio, 2024. "Learning fused lasso parameters in portfolio selection via neural networks," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4281-4299, October.
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