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A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk

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Abstract

The complexity involved in portfolio selection has resulted in the development of a large number of methods to support ambiguous financial decision making. We consider portfolio selection problems where returns from investment securities are random variables with fuzzy information and propose a data envelopment analysis model for portfolio selection with downside risk criteria associated with value-at-risk (V@R) and conditional value-at-risk (CV@R). Both V@R and CV@R criteria are used to define possibility, necessity, and credibility measures, which are formulated as stochastic nonlinear programming programs with random-fuzzy variables. Our constructed stochastic nonlinear programs for analyzing portfolio selection are transformed into deterministic nonlinear programs. Moreover, we show an enumeration algorithm can solve the model without any mathematical programs. Finally, we demonstrate the applicability of the proposed framework and the efficacy of the procedures with a numerical example.

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Notes

  1. If \( \varphi = Pos \) in Eq. (4), then a V@R-Possibility measure is described as

    \( \hbox{min} \,\,f\,\;s.t.\quad Pos\left[ {V@R_{\alpha } \left[ {\sum\limits_{j = 1}^{n} {x_{j} \tilde{r}_{j} } } \right] \le \,f} \right] \ge \beta \,,\,\;E\,\left[ {\sum\limits_{j = 1}^{n} {x_{j} \tilde{r}_{j} } } \right] \ge \eta ,\;\;\sum\limits_{j = 1}^{n} {x_{j} } = 1,\quad \,x_{j} \ge 0,\,\,\,j = 1, \ldots ,n.\, \)

  2. When we refer to a measure, we use V@R instead of \( V@R_{\alpha } \) for simplicity. This applies to the case of CV@R.

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Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions. Dr. Madjid Tavana is grateful for the partial support he received from the Czech Science Foundation (GAČR 19-13946S) for this research. Dr. Khanjani Shiraz received a grant from the Ministry of science, Research and Technology of the Islamic Republic of Iran in partial support of this research.

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Authors and Affiliations

  1. School of Mathematics Science, University of Tabriz, Tabriz, Iran

    Rashed Khanjani Shiraz

  2. Business Systems and Analytics Department, Distinguished Chair of Business Analytics, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  3. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098, Paderborn, Germany

    Madjid Tavana

  4. Department of Business Management, Faculty of Commerce, Fukuoka University, Fukuoka, Japan

    Hirofumi Fukuyama

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  1. Rashed Khanjani Shiraz
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  2. Madjid Tavana
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  3. Hirofumi Fukuyama
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Correspondence to Madjid Tavana.

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Khanjani Shiraz, R., Tavana, M. & Fukuyama, H. A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk. Soft Comput 24, 17167–17186 (2020). https://doi.org/10.1007/s00500-020-05010-7

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