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

Lesly Lisset Ortiz-Cerezo; Alin Andrei Carsteanu; Julio Bernardo Clempner

doi:10.3390/math10183221

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

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

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Translated title of the contribution	Cartera de relaciones de Sharpe en cadenas de Markov controlables: enfoque analítico y algorítmico para la programación de conos de segundo orden
Original language	English
Article number	3221
Journal	Mathematics
Volume	10
Issue number	18
DOIs	https://doi.org/10.3390/math10183221
State	Published - Sep 2022

Keywords

Markov chains
Markowitz
Sharpe ratio
fractional programming
optimization
portfolio

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10.3390/math10183221

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

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{\textquoteright}s efficiency and efficacy are demonstrated using a numerical example.",

keywords = "Markov chains, Markowitz, Sharpe ratio, fractional programming, optimization, portfolio",

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AU - Clempner, Julio Bernardo

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N2 - 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.

AB - 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.

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

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