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

Lesly Lisset Ortiz-Cerezo, Alin Andrei Carsteanu and Julio Bernardo Clempner ()
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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

Mathematics, 2022, vol. 10, issue 18, 1-13

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.

Keywords: portfolio; Sharpe ratio; Markowitz; fractional programming; Markov chains; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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