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Adaptive \(l_1\)-regularization for short-selling control in portfolio selection

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Abstract

We consider the \(l_1\)-regularized Markowitz model, where a \(l_1\)-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 \(l_1\)-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.

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Notes

  1. http://www.gurobi.com.

  2. Data available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#BookEquity

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Acknowledgements

This work was partially supported by FFABR grant, annuity 2017, and INdAM-GNCS Project 2018.

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Authors and Affiliations

  1. Department of Management and Quantitative Studies, University of Naples “Parthenope”, Naples, Italy

    Stefania Corsaro

  2. Department of Mathematics and Physics, University of Campania Luigi Vanvitelli, Caserta, Italy

    Valentina De Simone

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  1. Stefania Corsaro
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  2. Valentina De Simone
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Correspondence to Stefania Corsaro.

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Corsaro, S., De Simone, V. Adaptive \(l_1\)-regularization for short-selling control in portfolio selection. Comput Optim Appl 72, 457–478 (2019). https://doi.org/10.1007/s10589-018-0049-4

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  • DOI: https://doi.org/10.1007/s10589-018-0049-4

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