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Non-Monotonicity of the Tversky-Kahneman Probability-Weighting Function: A Cautionary Note

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  • Jonathan Ingersoll
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    Abstract

    "Cumulative Prospect Theory has gained a great deal of support as an alternative to Expected Utility Theory as it accounts for a number of anomalies in the observed behavior of economic agents. Expected Utility Theory uses a utility function and subjective or objective probabilities to compare risky prospects. Cumulative Prospect Theory alters both of these aspects. The concave utility function is replaced by a loss-averse utility function and probabilities are replaced by decision weights. The latter are determined with a weighting function applied to the cumulative probability of the outcomes. Several different probability weighting functions have been suggested. The two most popular are the original proposal of Tversky and Kahneman and the compound-invariant form proposed by Prelec. This note shows that the Tversky-Kahneman probability weighting function is not increasing for all parameter values and therefore can assign negative decision weights to some outcomes. This in turn implies that Cumulative Prospect Theory could make choices not consistent with first-order stochastic dominance". Copyright (c) 2008 The Author Journal compilation (c) 2008 Blackwell Publishing Ltd.

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    Bibliographic Info

    Article provided by European Financial Management Association in its journal European Financial Management.

    Volume (Year): 14 (2008)
    Issue (Month): 3 ()
    Pages: 385-390

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    Handle: RePEc:bla:eufman:v:14:y:2008:i:3:p:385-390

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    Cited by:
    1. Santos-Pinto, Luís & Astebro, Thomas & Mata, José, 2009. "Preference for Skew in Lotteries: Evidence from the Laboratory," MPRA Paper 17165, University Library of Munich, Germany.
    2. Salvatore Greco & Fabio Rindone, 2014. "The bipolar Choquet integral representation," Theory and Decision, Springer, vol. 77(1), pages 1-29, June.
    3. 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.
    4. Daniel Cavagnaro & Mark Pitt & Richard Gonzalez & Jay Myung, 2013. "Discriminating among probability weighting functions using adaptive design optimization," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 255-289, December.
    5. Bahaji, Hamza, 2014. "Are Employee Stock Option Exercise Decisions Better Explained through the Prospect Theory?," Economics Papers from University Paris Dauphine 123456789/13098, Paris Dauphine University.
    6. De Giorgi, Enrico & Hens, Thorsten & Rieger, Marc Oliver, 2010. "Financial market equilibria with cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 633-651, September.
    7. 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.
    8. Dichtl, Hubert & Drobetz, Wolfgang, 2011. "Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1683-1697, July.
    9. Rieger, Marc Oliver, 2014. "Evolutionary stability of prospect theory preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 1-11.
    10. Greco, Salvatore & Rindone, Fabio, 2011. "The bipolar Choquet integral representation," MPRA Paper 38957, University Library of Munich, Germany, revised 14 Oct 2011.
    11. Matteo Del Vigna, 2011. "Financial market equilibria with heterogeneous agents: CAPM and market segmentation," Working Papers - Mathematical Economics 2011-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    12. Bahaji, Hamza, 2012. "Cumulative Prospect Theory, employee exercise behaviour and stock options cost assessment," Economics Papers from University Paris Dauphine 123456789/9550, Paris Dauphine University.

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