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The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number

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  • Krzysztof Piasecki
  • Joanna Siwek

Abstract

A multi-asset portfolio in the case of its present value estimated by a discrete trapezoidal fuzzy number has been assessed. The benefits of owning a security have been evaluated according to an expected fuzzy discount factor. The ambiguity risk has been assessed by an energy measure and indistinctness risk has been evaluated by Kosko’s entropy measure. The relationship between the expected fuzzy discount factor for a portfolio and the expected fuzzy discount factors for its components has been derived. An analogous relationship between the values of the energy measure has been presented. The model has been illustrated by means of a profound numerical case study.

Suggested Citation

  • Krzysztof Piasecki & Joanna Siwek, 2018. "The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 57-74.
    • Handle: RePEc:wut:journl:v:1:y:2018:p:57-74:id:1346
    DOI: 10.5277/ord180104
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    References listed on IDEAS

    as
    1. Liu, Yong-Jun & Zhang, Wei-Guo, 2013. "Fuzzy portfolio optimization model under real constraints," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 704-711.
    2. Krzysztof Piasecki, 2013. "Behavioural present value," Papers 1302.0539, arXiv.org.
    3. Krzysztof M. Piasecki, 2011. "Effectiveness of securities with fuzzy probabilistic return," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(2), pages 65-78.
    4. Seymour Kaplan & Norman N. Barish, 1967. "Decision-Making Allowing for Uncertainty of Future Investment Opportunities," Management Science, INFORMS, vol. 13(10), pages 569-577, June.
    5. Krzysztof Piasecki, 2012. "The basis of financial arithmetic from the viewpoint of utility theory," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(3), pages 37-53.
    6. Gutiérrez, Isabel, 1989. "Fuzzy numbers and net present value," Scandinavian Journal of Management, Elsevier, vol. 5(2), pages 149-159.
    7. Yong Fang & Kin Keung Lai & Shouyang Wang, 2008. "Fuzzy Portfolio Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-77926-1, October.
    8. Piasecki Krzysztof & Siwek Joanna, 2015. "Behavioural Present Value Defined as Fuzzy Number – a New Approach," Folia Oeconomica Stetinensia, Sciendo, vol. 15(2), pages 27-41, December.
    9. Huang, Xiaoxia, 2007. "Two new models for portfolio selection with stochastic returns taking fuzzy information," European Journal of Operational Research, Elsevier, vol. 180(1), pages 396-405, July.
    10. Guo, Sini & Yu, Lean & Li, Xiang & Kar, Samarjit, 2016. "Fuzzy multi-period portfolio selection with different investment horizons," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1026-1035.
    11. repec:wut:journl:v:3:y:2012:id:1044 is not listed on IDEAS
    12. Piasecki, Krzysztof, 2011. "Effectiveness of securities with fuzzy probabilistic return," MPRA Paper 46214, University Library of Munich, Germany.
    13. Cédric Lesage, 2001. "Discounted cash-flows analysis: An interactive fuzzy arithmetic approach," Post-Print hal-00485731, HAL.
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