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

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  • Jonathan Ingersoll

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.

Suggested Citation

  • Jonathan Ingersoll, 2008. "Non-Monotonicity of the Tversky-Kahneman Probability-Weighting Function: A Cautionary Note," European Financial Management, European Financial Management Association, vol. 14(3), pages 385-390.
  • Handle: RePEc:bla:eufman:v:14:y:2008:i:3:p:385-390
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    Cited by:

    1. Kelvin Balcombe & Iain Fraser, 2015. "Parametric preference functionals under risk in the gain domain: A Bayesian analysis," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 161-187, April.
    2. Salvatore Greco & Fabio Rindone, 2014. "The bipolar Choquet integral representation," Theory and Decision, Springer, vol. 77(1), pages 1-29, June.
    3. Martina Nardon & Paolo Pianca, 2015. "Probability weighting functions," Working Papers 2015:29, Department of Economics, University of Venice "Ca' Foscari".
    4. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-016-2127-2 is not listed on IDEAS
    5. repec:dau:papers:123456789/13098 is not listed on IDEAS
    6. 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.
    7. Roger J. Jiao & Feng Zhou & Chih-Hsing Chu, 0. "Decision theoretic modeling of affective and cognitive needs for product experience engineering: key issues and a conceptual framework," Journal of Intelligent Manufacturing, Springer, vol. 0, pages 1-13.
    8. Thomas Astebro & José Mata & Luis Santos-Pinto, 2009. "Preference for Skew in Lotteries: Evidence from the Laboratory," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 09.09, Université de Lausanne, Faculté des HEC, DEEP.
    9. Rieger, Marc Oliver, 2014. "Evolutionary stability of prospect theory preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 1-11.
    10. 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.
    11. 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.
    12. 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.
    13. repec:kap:theord:v:82:y:2017:i:4:d:10.1007_s11238-016-9582-8 is not listed on IDEAS
    14. Bahaji, Hamza & Casta, Jean-François, 2016. "Employee stock option-implied risk attitude under Rank-Dependent Expected Utility," Economic Modelling, Elsevier, vol. 52(PA), pages 144-154.
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    16. 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.
    17. Behnam Malakooti, 2015. "Double Helix Value Functions, Ordinal/Cardinal Approach, Additive Utility Functions, Multiple Criteria, Decision Paradigm, Process, and Types (Z Theory I)," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1353-1400, November.
    18. 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.
    19. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "The role of a representative reinsurer in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 196-204.
    20. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    21. repec:eee:enepol:v:111:y:2017:i:c:p:414-426 is not listed on IDEAS

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