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Renyi entropy of uncertain random variables and its application to portfolio selection

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Abstract

This paper proposes a new type of entropy called Renyi entropy as an extension of logarithm entropy in an uncertain random environment and applies it to portfolio selection. We first define Renyi entropy and partial Renyi entropy to measure the indeterminacy of uncertain random variables and examine their mathematical properties. Then, we provide an approach for calculating partial Renyi entropy for uncertain random variables through Monte Carlo simulation. Next, we introduce Renyi cross-entropy and the concept of partial Renyi cross-entropy of uncertain random variables. As an application in finance, partial Renyi entropy is invoked to optimize portfolio selection of uncertain random returns. Numerical examples are displayed for illustration purposes. Finally, we compare the investment strategies adopted by the mean-Renyi entropy models with those of the mean-elliptic entropy models and the mean-variance models.

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Acknowledgements

The authors would like to thank the referees for their valuable comments which helped to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia

    Souad Chennaf

  2. Telecommunications High School of Tunis, Technological City of Communications, Tunis, Tunisia

    Jaleleddine Ben Amor

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  1. Souad Chennaf
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  2. Jaleleddine Ben Amor
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The conceptualization, writing and formal analysis were done by SC. The methodology, editing and improving the language were carried out by JBA. All authors read and reviewed the manuscript.

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Correspondence to Souad Chennaf.

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Chennaf, S., Ben Amor, J. Renyi entropy of uncertain random variables and its application to portfolio selection. Soft Comput 27, 11569–11585 (2023). https://doi.org/10.1007/s00500-023-08120-0

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