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Time-Varying Mean-Variance Portfolio Selection under Transaction Costs and Cardinality Constraint Problem via Beetle Antennae Search Algorithm (BAS)

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Abstract

The Markowitz mean-variance portfolio selection is widely acclaimed as a very important investment strategy. A popular option to solve the static mean-variance portfolio selection (MVPS) problem is based on the use of quadratic programming (QP) methods. On the other hand, the static portfolio selection under transaction costs (PSTC) problem is usually approached with nonlinear programming (NLP) methods. In this article, we define and study the time-varying mean-variance portfolio selection under transaction costs and cardinality constraint (TV-MVPSTC-CC) problem as a time-varying nonlinear programming (TVNLP) problem. The TV-MVPSTC-CC also comprises the properties of a moving average. These properties make the TV-MVPSTC-CC an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using the Beetle Antennae Search (BAS) algorithm, we also provide an online solution to the static NLP problem. To the best of our knowledge, this is an innovative approach that incorporates modern meta-heuristic optimization techniques to provide an online, thus more realistic, solution to the TV-MVPSTC-CC problem. In this way, we present an online solution to a time-varying financial problem while eliminating the restrictions of static methods. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to traditional approaches.

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Acknowledgements

Predrag Stanimirović acknowledges support from the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013.

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Authors and Affiliations

  1. Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559, Athens, Greece

    Vasilios N. Katsikis & Spyridon D. Mourtas

  2. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Predrag S. Stanimirović

  3. Swansea University, Swansea, UK

    Shuai Li

  4. School of Management, Shanghai University, Shanghai, China

    Xinwei Cao

Authors
  1. Vasilios N. Katsikis
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  2. Spyridon D. Mourtas
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  3. Predrag S. Stanimirović
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Correspondence to Vasilios N. Katsikis.

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Katsikis, V.N., Mourtas, S.D., Stanimirović, P.S. et al. Time-Varying Mean-Variance Portfolio Selection under Transaction Costs and Cardinality Constraint Problem via Beetle Antennae Search Algorithm (BAS). SN Oper. Res. Forum 2, 18 (2021). https://doi.org/10.1007/s43069-021-00060-5

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  • DOI: https://doi.org/10.1007/s43069-021-00060-5

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