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An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories

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  • Harin, Alexander

Abstract

An existence theorem is proved for the case of a discrete random variable with finite support. If the random variable takes on values in a finite interval and there is a lower non-zero bound on its dispersion, then non-zero bounds (or non-zero “forbidden zones”) on its expectation exist near the borders of the interval. The theorem can be used in utility and prospect theories, in particular, in the analysis of Prelec’s probability weighting function.

Suggested Citation

  • Harin, Alexander, 2015. "An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories," MPRA Paper 66692, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:66692
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    File URL: https://mpra.ub.uni-muenchen.de/66692/1/MPRA_paper_66692.pdf
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    References listed on IDEAS

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    1. Alexander Harin, 2012. "Data Dispersion in Economics(II) - Inevitability and Consequences of Restrictions," Review of Economics & Finance, Better Advances Press, Canada, vol. 2, pages 24-36, November.
    2. Daniel Kahneman & Richard H. Thaler, 2006. "Anomalies: Utility Maximization and Experienced Utility," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 221-234, Winter.
    3. Schoemaker, Paul J. H. & Hershey, John C., 1992. "Utility measurement: Signal, noise, and bias," Organizational Behavior and Human Decision Processes, Elsevier, vol. 52(3), pages 397-424, August.
    4. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
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    Cited by:

    1. Harin, Alexander, 2015. "An existence theorem for bounds on the expectation of a random variable. Its opportunities for utility theories. V. 2," MPRA Paper 67071, University Library of Munich, Germany.

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    More about this item

    Keywords

    probability theory; dispersion; scatter; scattering; noise; economics; utility theory; prospect theory; decision theories; human behavior; Prelec; probability weighting function;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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