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An existence theorem for bounds on the expectation of a random variable. Its opportunities for utility theories. V. 2

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  • Harin, Alexander

Abstract

An existence theorem is proven for the case of a discrete random variable that can take on only a finite set of possible values. If the random variable takes on values in a finite interval and there is a lower non-zero bound on the modulus of (at least one) its central moment, then non-zero bounds on its expectation exist near the borders of the interval. The revealed bounds can be considered as “forbidden zones” for the expectation. They can be useful, e.g., in utility theories.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:67071
    as

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    File URL: https://mpra.ub.uni-muenchen.de/67071/1/MPRA_paper_67071.pdf
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    References listed on IDEAS

    as
    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. 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.
    5. 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.
    6. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    Full references (including those not matched with items on IDEAS)

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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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