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A chance-constrained portfolio selection model with random-rough variables

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Abstract

Traditional portfolio selection (PS) models are based on the restrictive assumption that the investors have precise information necessary for decision-making. However, the information available in the financial markets is often uncertain. This uncertainty is primarily the result of unquantifiable, incomplete, imprecise, or vague information. The uncertainty associated with the returns in PS problems can be addressed using random-rough (Ra-Ro) variables. We propose a new PS model where the returns are stochastic variables with rough information. More precisely, we formulate a Ra-Ro mathematical programming model where the returns are represented by Ra-Ro variables and the expected future total return maximized against a given fractile probability level. The resulting change-constrained (CC) formulation of the PS optimization problem is a non-linear programming problem. The proposed solution method transforms the CC model in an equivalent deterministic quadratic programming problem using interval parameters based on optimistic and pessimistic trust levels. As an application of the proposed method and to show its flexibility, we consider a probability maximizing version of the PS problem where the goal is to maximize the probability that the total return is higher than a given reference value. Finally, a numerical example is provided to further elucidate how the solution method works.

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Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions. The second author, Dr. Khanjani Shiraz, is grateful to the Iran National Science Foundation for the support he received through grant number 93040776.

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Authors and Affiliations

  1. Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

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

    Madjid Tavana

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

    Rashed Khanjani Shiraz

  4. Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Debora Di Caprio

  5. Polo Tecnologico IISS G. Galilei, Via Cadorna 14, 39100, Bolzano, Italy

    Debora Di Caprio

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  1. Madjid Tavana
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  3. Debora Di Caprio
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Correspondence to Madjid Tavana.

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Tavana, M., Khanjani Shiraz, R. & Di Caprio, D. A chance-constrained portfolio selection model with random-rough variables. Neural Comput & Applic 31 (Suppl 2), 931–945 (2019). https://doi.org/10.1007/s00521-017-3014-8

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