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Lottery valuation using the aspiration / relative utility function

Author

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  • Krzysztof Kontek

    (Artal Investments)

Abstract

The paper presents a method for lottery valuation using the relative utility function. This function was presented by Kontek (2009) as “the aspiration function” and resembles the utility curve proposed by Markowitz (1952A). The paper discusses lotteries with discrete and continuous outcome distributions as well as lotteries with positive, negative and mixed outcomes providing analytical formulas for certainty equivalents in each case. The solution is similar to the Expected Utility Theory approach and does not use the probability weighting function – one of the key elements of Prospect Theory. Solutions to several classical behavioral problems, including the Allais paradox, are presented, demonstrating that the method can be used for valuing lotteries even in more complex cases of outcomes described by a combination of Beta distributions. The paper provides strong arguments against Prospect Theory as a model for describing human behavior and lays the foundations for Relative Utility Theory – a new theory of decision making under conditions of risk.

Suggested Citation

  • Krzysztof Kontek, 2009. "Lottery valuation using the aspiration / relative utility function," Working Papers 39, Department of Applied Econometrics, Warsaw School of Economics.
    • Handle: RePEc:wse:wpaper:39
    as

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    File URL: http://kolegia.sgh.waw.pl/pl/KAE/struktura/IE/struktura/ZES/Documents/Working_Papers/aewp05-09.pdf
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    References listed on IDEAS

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    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    3. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 97-122, February.
    4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    5. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
    6. Kontek, Krzysztof, 2009. "On Mental Transformations," MPRA Paper 16516, University Library of Munich, Germany.
    7. 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..
    8. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
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    Cited by:

    1. Toritseju Begho & Kelvin Balcombe, 2023. "Attitudes to Risk and Uncertainty: New Insights From an Experiment Using Interval Prospects," SAGE Open, , vol. 13(3), pages 21582440231, July.
    2. Kontek, Krzysztof, 2010. "Mean, Median or Mode? A Striking Conclusion From Lottery Experiments," MPRA Paper 21758, University Library of Munich, Germany.
    3. Kontek, Krzysztof, 2010. "Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility," MPRA Paper 22947, University Library of Munich, Germany.
    4. Kontek, Krzysztof, 2010. "Density Based Regression for Inhomogeneous Data: Application to Lottery Experiments," MPRA Paper 22268, University Library of Munich, Germany.
    5. Kontek, Krzysztof, 2009. "Absolute vs. Relative Notion of Wealth Changes," MPRA Paper 17336, University Library of Munich, Germany.

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    More about this item

    Keywords

    Lottery Valuation; Expected Utility Theory; Markowitz Hypothesis; Prospect / Cumulative Prospect Theory; Aspiration / Relative Utility Function;
    All these keywords.

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