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How to solve the St Petersburg Paradox in Rank-Dependent Models ?

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  • Marie Pfiffelmann

    (Laboratoire de Recherche en Gestion et Economie, Université Louis Pasteur)

Abstract

The Cumulative Prospect Theory, as it was specified by Tversky and Kahneman (1992) does not explain the St Petersburg Paradox. This study shows that the solutions proposed in the literature (Blavatskky, 2005; Rieger and Wang, 2006) to guarantee, under rank dependant models, finite subjective utilities for any prospects with finite expected values have to cope with many limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggested to replace the weighting function generally proposed in the literature with another specification which respects the following properties. 1) In order to guarantee finite subjective values for all prospects with finite expected values, the slope at zero should be finite. 2) To account for the fourfold pattern of risk attitudes, the probability weighting should be strong enough to overcome the concavity of the value function.

Suggested Citation

  • Marie Pfiffelmann, 2007. "How to solve the St Petersburg Paradox in Rank-Dependent Models ?," Working Papers of LaRGE Research Center 2007-08, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    • Handle: RePEc:lar:wpaper:2007-08
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    References listed on IDEAS

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    1. Marie Pfiffelmann, 2006. "Which Optimal Design For LLDAs?," Working Papers of LaRGE Research Center 2006-06, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    2. Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 136-138.
    3. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    5. Neilson, William S & Stowe, Jill, 2002. "A Further Examination of Cumulative Prospect Theory Parameterizations," Journal of Risk and Uncertainty, Springer, vol. 24(1), pages 31-46, January.
    6. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
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    Cited by:

    1. Marie Pfiffelmann, 2006. "Which Optimal Design For LLDAs?," Working Papers of LaRGE Research Center 2006-06, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.

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    More about this item

    Keywords

    St Petersburg Paradox; Cumulative Prospect Theory; Probability Weighting; Gambling.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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