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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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