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

Author

Listed:
  • Vasilios N. Katsikis

    (National and Kapodistrian University of Athens)

  • Spyridon D. Mourtas

    (National and Kapodistrian University of Athens)

  • Predrag S. Stanimirović

    (University of Niš)

  • Shuai Li

    (Swansea University)

  • Xinwei Cao

    (Shanghai University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:2:d:10.1007_s43069-021-00060-5
    DOI: 10.1007/s43069-021-00060-5
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    References listed on IDEAS

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    1. Miguel Lobo & Maryam Fazel & Stephen Boyd, 2007. "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, Springer, vol. 152(1), pages 341-365, July.
    2. Katsikis, Vasilios N. & Mourtas, Spyridon D., 2019. "A heuristic process on the existence of positive bases with applications to minimum-cost portfolio insurance in C[a, b]," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 221-244.
    3. Kai Ye & Panos Parpas & Berç Rustem, 2012. "Robust portfolio optimization: a conic programming approach," Computational Optimization and Applications, Springer, vol. 52(2), pages 463-481, June.
    4. Włodzimierz Ogryczak & Tomasz Śliwiński, 2011. "On solving the dual for portfolio selection by optimizing Conditional Value at Risk," Computational Optimization and Applications, Springer, vol. 50(3), pages 591-595, December.
    5. Katsikis, Vasilios N. & Mourtas, Spyridon D. & Stanimirović, Predrag S. & Li, Shuai & Cao, Xinwei, 2020. "Time-varying minimum-cost portfolio insurance under transaction costs problem via Beetle Antennae Search Algorithm (BAS)," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    6. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
    7. Zhifeng Dai, 2019. "A Closer Look at the Minimum-Variance Portfolio Optimization Model," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, August.
    8. 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.
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    Cited by:

    1. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Andrey V. Chukalin & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Portfolio Insurance through Error-Correction Neural Networks," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    2. Katsikis, Vasilios N. & Mourtas, Spyridon D. & Stanimirović, Predrag S. & Li, Shuai & Cao, Xinwei, 2023. "Time-varying minimum-cost portfolio insurance problem via an adaptive fuzzy-power LVI-PDNN," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "V-Shaped BAS: Applications on Large Portfolios Selection Problem," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1353-1373, December.
    4. Simos, Theodore E. & Katsikis, Vasilios N. & Mourtas, Spyridon D., 2022. "Multi-input bio-inspired weights and structure determination neuronet with applications in European Central Bank publications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 451-465.
    5. Spyridon D. Mourtas & Chrysostomos Kasimis, 2022. "Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-20, August.

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