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Parameter interactions in cumulative prospect theory in relation to probability weighting

Author

Listed:
  • Elżbieta Babula

    (UG - University of Gdańsk)

  • Juhyun Park

    (LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise)

Abstract

Tversky and Kahneman's cumulative prospect theory assumes symmetric probability cumulation with regard to the reference point in decision weights. Theoretically, this model should be fixed despite a change in the direction of probability cumulation. We investigate this phenomenon by proposing an alternative model with one-direction probability cumulation. By doing so, we create a reference model that allows us to verify the parameter interactions in cumulative prospect theory specifications. We apply the simultaneous parametric fitting of utility and weighting functions using binary choice data from our own incentivized choice experiment (N = 70). We consider two parametric forms of probability weighting functions, namely, the one-parameter Tversky–Kahneman and two-parameter Prelec functions. We find that the Prelec function is sufficiently flexible to make these two models equivalent, thereby preserving the stability of the utility parameters. We also observe parameter interactions in the other specifications, especially with the Tversky–Kahneman weighting function.

Suggested Citation

  • Elżbieta Babula & Juhyun Park, 2025. "Parameter interactions in cumulative prospect theory in relation to probability weighting," Post-Print hal-05231129, HAL.
    • Handle: RePEc:hal:journl:hal-05231129
    DOI: 10.14254/2071-789X.2025/18-2/6
    Note: View the original document on HAL open archive server: https://hal.science/hal-05231129v1
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    References listed on IDEAS

    as
    1. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, vol. 98(5), pages 2066-2100, December.
    2. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    3. Luce, R Duncan & Fishburn, Peter C, 1991. "Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 29-59, January.
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