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Effectiveness of securities with fuzzy probabilistic return

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  • Piasecki, Krzysztof

Abstract

The generalized fuzzy present value of a security is defined here as fuzzy valued utility of cash flow. The generalized fuzzy present value cannot depend on the value of future cash flow. There exists such a generalized fuzzy present value which is not a fuzzy present value in the sense given by Ward [35] or by Huang [14]. If the present value is a fuzzy number and the future value is a random variable, then the return rate is given as a probabilistic fuzzy subset on the real line. This kind of return rate is called a fuzzy probabilistic return. The main goal of this paper is to derive the family of effective securities with fuzzy probabilistic return. Achieving this goal requires the study of the basic parameters characterizing fuzzy probabilistic return. Therefore, fuzzy expected value and variance are determined for this case of return. These results are a starting point for constructing a three-dimensional image. The set of effective securities is introduced as the Pareto optimal set determined by the maximization of the expected return rate and minimization of the variance. Finally, the set of effective securities is distinguished as a fuzzy set. These results are obtained without the assumption that the distribution of future values is Gaussian.

Suggested Citation

  • Piasecki, Krzysztof, 2011. "Effectiveness of securities with fuzzy probabilistic return," MPRA Paper 46214, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:46214
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Gutiérrez, Isabel, 1989. "Fuzzy numbers and net present value," Scandinavian Journal of Management, Elsevier, vol. 5(2), pages 149-159.
    5. Kontek, Krzysztof, 2010. "Decision Utility Theory: Back to von Neumann, Morgenstern, and Markowitz," MPRA Paper 27141, University Library of Munich, Germany.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    8. Krzysztof Piasecki, 2013. "Behavioural present value," Papers 1302.0539, arXiv.org.
    9. Cédric Lesage, 2001. "Discounted cash-flows analysis: An interactive fuzzy arithmetic approach," Post-Print hal-00485731, HAL.
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    Cited by:

    1. 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.
    2. Anna Łyczkowska-Hanćkowiak, 2019. "Sharpe’s Ratio for Oriented Fuzzy Discount Factor," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    3. 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.
    4. repec:wut:journl:v:3:y:2012:id:1044 is not listed on IDEAS

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    More about this item

    Keywords

    behavioural present value; fuzzy present value; random future value; fuzzy probabilistic return; effective financial security.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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