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Adaptive $$l_1$$ l 1 -regularization for short-selling control in portfolio selection

Author

Listed:
  • Stefania Corsaro

    (University of Naples “Parthenope”)

  • Valentina Simone

    (University of Campania Luigi Vanvitelli)

Abstract

We consider the $$l_1$$ l 1 -regularized Markowitz model, where a $$l_1$$ l 1 -penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution. The $$l_1$$ l 1 -penalty term can also be interpreted in terms of short sales, on which several financial markets have posed restrictions. The choice of the regularization parameter plays a key role to obtain optimal portfolios that meet the financial requirements. We propose an updating rule for the regularization parameter in Bregman iteration to control both the sparsity and the number of short positions. We show that the modified scheme preserves the properties of the original one. Numerical tests are reported, which show the effectiveness of the approach.

Suggested Citation

  • Stefania Corsaro & Valentina Simone, 2019. "Adaptive $$l_1$$ l 1 -regularization for short-selling control in portfolio selection," Computational Optimization and Applications, Springer, vol. 72(2), pages 457-478, March.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0049-4
    DOI: 10.1007/s10589-018-0049-4
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    References listed on IDEAS

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    Cited by:

    1. Vasilios N. Katsikis & Spyridon D. Mourtas & Predrag S. Stanimirović & Shuai Li & Xinwei Cao, 2021. "Time-Varying Mean-Variance Portfolio Selection under Transaction Costs and Cardinality Constraint Problem via Beetle Antennae Search Algorithm (BAS)," SN Operations Research Forum, Springer, vol. 2(2), pages 1-26, June.
    2. Bernardo K. Pagnoncelli & Felipe del Canto & Arturo Cifuentes, 2021. "The effect of regularization in portfolio selection problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 156-176, April.
    3. 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.
    4. Stefania Corsaro & Valentina De Simone & Zelda Marino & Salvatore Scognamiglio, 2022. "l 1 -Regularization in Portfolio Selection with Machine Learning," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    5. 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).
    6. Stefania Corsaro & Valentina De Simone & Zelda Marino, 2021. "Fused Lasso approach in portfolio selection," Annals of Operations Research, Springer, vol. 299(1), pages 47-59, April.

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