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Sharpe-Ratio Portfolio in Controllable Markov Chains: Analytic and Algorithmic Approach for Second Order Cone Programming

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  • Lesly Lisset Ortiz-Cerezo

    (Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, School of Physics and Mathematics, Mexico City 07730, Mexico)

  • Alin Andrei Carsteanu

    (Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, School of Physics and Mathematics, Mexico City 07730, Mexico)

  • Julio Bernardo Clempner

    (Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, School of Physics and Mathematics, Mexico City 07730, Mexico)

Abstract

The Sharpe ratio is a measure based on the theory of mean variance, it is the measure of the performance of a portfolio when the risk can be measured through the standard deviation. This paper suggests a Sharpe-ratio portfolio solution using a second order cone programming (SOCP). We use the penalty-regularized method to represent the nonlinear portfolio problem. We present a computationally tractable way to determining the Sharpe-ratio portfolio. A Markov chain structure is employed to represent the underlying asset price process. In order to determine the optimal portfolio in Markov chains, a new hybrid optimization programming method for SOCP is proposed. The suggested method’s efficiency and efficacy are demonstrated using a numerical example.

Suggested Citation

  • Lesly Lisset Ortiz-Cerezo & Alin Andrei Carsteanu & Julio Bernardo Clempner, 2022. "Sharpe-Ratio Portfolio in Controllable Markov Chains: Analytic and Algorithmic Approach for Second Order Cone Programming," Mathematics, MDPI, vol. 10(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3221-:d:907670
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    References listed on IDEAS

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    1. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    2. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    3. Marianne Akian & Agnès Sulem & Michael I. Taksar, 2001. "Dynamic Optimization of Long‐Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 153-188, April.
    4. B. Fastrich & S. Paterlini & P. Winker, 2015. "Constructing optimal sparse portfolios using regularization methods," Computational Management Science, Springer, vol. 12(3), pages 417-434, July.
    5. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    6. George M. Constantinides, 1979. "Multiperiod Consumption and Investment Behavior with Convex Transactions Costs," Management Science, INFORMS, vol. 25(11), pages 1127-1137, November.
    7. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    8. Caruso, G. & Gattone, S.A. & Fortuna, F. & Di Battista, T., 2021. "Cluster Analysis for mixed data: An application to credit risk evaluation," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    9. Kourtis, Apostolos, 2016. "The Sharpe ratio of estimated efficient portfolios," Finance Research Letters, Elsevier, vol. 17(C), pages 72-78.
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