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Cumulative prospect theory and the St. Petersburg paradox

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  • Marc Rieger

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  • Mei Wang

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    Abstract

    We find that in cumulative prospect theory (CPT) with a concave value function in gains, a lottery with finite expected value may have infinite subjective value. This problem does not occur in expected utility theory. The paradox occurs in particular in the setting and the parameter regime studied by Tversky and Kahneman [15] and in subsequent works. We characterize situations in CPT where the problem can be resolved. In particular, we define a class of admissible probability distributions and admissible parameter regimes for the weighting- and value functions for which finiteness of the subjective value can be proved. Alternatively, we suggest a new weighting function for CPT which guarantees finite subjective value for all lotteries with finite expected value, independent of the choice of the value function. Some of these results have already been found independently by Blavatskyy [4] in the context of discrete lotteries. Copyright Springer-Verlag Berlin/Heidelberg 2006

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    Bibliographic Info

    Article provided by Springer in its journal Economic Theory.

    Volume (Year): 28 (2006)
    Issue (Month): 3 (08)
    Pages: 665-679

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    Handle: RePEc:spr:joecth:v:28:y:2006:i:3:p:665-679

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    Related research

    Keywords: Cumulative prospect theory; Probability weighting function; St. Petersburg paradox.;

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    Cited by:
    1. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabeth E., 2007. "Behavioral Econometrics for Psychologists," Working Papers 18-2007, Copenhagen Business School, Department of Economics.
    2. Galarza, Francisco, 2009. "Choices under Risk in Rural Peru," MPRA Paper 17708, University Library of Munich, Germany.
    3. Lewandowski, Michal, 2006. "Is Cumulative Prospect Theory a Serious Alternative for the Expected Utility Paradigm?," MPRA Paper 43271, University Library of Munich, Germany.
    4. James C. Cox & Vjollca Sadiraj & Bodo Vogt, 2009. "On the empirical relevance of st. petersburg lotteries," Economics Bulletin, AccessEcon, vol. 29(1), pages 214-220.
    5. : Constantinos Antoniou & : Glenn W. Harrison & : Morten I. Lau & : Daniel Read, 2013. "Subjective Bayesian Beliefs," Working Papers wpn13-02, Warwick Business School, Finance Group.
    6. Greco, Salvatore & Rindone, Fabio, 2011. "The bipolar Choquet integral representation," MPRA Paper 38957, University Library of Munich, Germany, revised 14 Oct 2011.
    7. Salvatore Greco & Fabio Rindone, 2014. "The bipolar Choquet integral representation," Theory and Decision, Springer, vol. 77(1), pages 1-29, June.
    8. Marie Pfiffelmann, 2011. "Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting," Theory and Decision, Springer, vol. 71(3), pages 325-341, September.
    9. Wang, Qian & Sundberg, Marcus & Karlström, Anders, 2013. "Scheduling choices under rank dependent utility maximization," Working papers in Transport Economics 2013:16, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
    10. Connors, Richard D. & Sumalee, Agachai, 2009. "A network equilibrium model with travellers' perception of stochastic travel times," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 614-624, July.
    11. James Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2013. "Is there a plausible theory for decision under risk? A dual calibration critique," Economic Theory, Springer, vol. 54(2), pages 305-333, October.
    12. Marc Scholten & Daniel Read, 2014. "Prospect theory and the “forgotten” fourfold pattern of risk preferences," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 67-83, February.
    13. Mattos, Fabio & Garcia, Philip & Pennings, Joost M.E., 2008. "Probability weighting and loss aversion in futures hedging," Journal of Financial Markets, Elsevier, vol. 11(4), pages 433-452, November.
    14. Xiaoxian Ma & Qingzhen Zhao & Jilin Qu, 2008. "Robust portfolio optimization with a generalized expected utility model under ambiguity," Annals of Finance, Springer, vol. 4(4), pages 431-444, October.
    15. Gürtler, Marc & Stolpe, Julia, 2011. "Piecewise continuous cumulative prospect theory and behavioral financial engineering," Working Papers IF37V1, Technische Universität Braunschweig, Institute of Finance.
    16. Peel, D.A., 2013. "Heterogeneous agents and the implications of the Markowitz model of utility for multi-prize lottery tickets," Economics Letters, Elsevier, vol. 119(3), pages 264-267.
    17. Takahashi, Taiki, 2009. "Tsallis’ non-extensive free energy as a subjective value of an uncertain reward," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 715-719.
    18. Azevedo, Eduardo M. & Gottlieb, Daniel, 2012. "Risk-neutral firms can extract unbounded profits from consumers with prospect theory preferences," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1291-1299.
    19. Kaivanto, Kim, 2008. "Alternation Bias and the Parameterization of Cumulative Prospect Theory," EconStor Open Access Articles, ZBW - German National Library of Economics, pages 91-107.

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