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Separating curvature and elevation: A parametric probability weighting function

Author

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  • Olivier L'Haridon

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Mohammed Abdellaoui

    () (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Horst Zank

    (Department of Applied Economics - Erasmus University Rotterdam)

Abstract

This paper presents a preference foundation for a two-parameter family of probability weighting functions. We provide a theoretical link between the well-established notions of probabilistic risk attitudes (i.e., optimism and pessimism) used in economics and the important independent measures for individual behavior used in the psychology literature (i.e., curvature and elevation). One of the parameters in our model measures curvature and represents the diminishing effect of optimism and pessimism when moving away from extreme probabilities 0 and 1. The other parameter measures elevation and represents the relative strength of optimism vs. pessimism. Our empirical analysis indicates that the new weighting function fits elicited probability weights well, and that it can explain differences in the treatment of probabilities for gains compared to that for probabilities of losses.

Suggested Citation

  • Olivier L'Haridon & Mohammed Abdellaoui & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Post-Print hal-00528381, HAL.
  • Handle: RePEc:hal:journl:hal-00528381
    DOI: 10.1007/s11166-010-9097-6
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00528381
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Nathalie Etchart-Vincent & Olivier l’Haridon, 2011. "Monetary incentives in the loss domain and behavior toward risk: An experimental comparison of three reward schemes including real losses," Journal of Risk and Uncertainty, Springer, vol. 42(1), pages 61-83, February.
    2. Kim Kaivanto, 2014. "Visceral emotions, within-community communication, and (ill-judged) endorsement of financial propositions," Working Papers 69123498, Lancaster University Management School, Economics Department.
    3. Vieider, Ferdinand M., 2012. "Moderate stake variations for risk and uncertainty, gains and losses: Methodological implications for comparative studies," Economics Letters, Elsevier, vol. 117(3), pages 718-721.
    4. Manel Baucells & Franz H. Heukamp, 2012. "Probability and Time Trade-Off," Management Science, INFORMS, vol. 58(4), pages 831-842, April.
    5. Gigi Foster & Paul Frijters & Markus Schaffner & Benno Torgler, 2013. "Expectation Formation in an Evolving Game of Uncertainty: Theory and New Experimental Evidence," QuBE Working Papers 022, QUT Business School.
    6. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    7. Dmitri Vinogradov & Yousef Makhlouf, 2017. "Signaling Probabilities in Ambiguity: on the impact of vague news," Working Papers 2017_12, Business School - Economics, University of Glasgow.
    8. Craig Webb, 2015. "Piecewise additivity for non-expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 371-392, October.
    9. Dennery, Charles & Direr, Alexis, 2014. "Optimal lottery," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 15-23.
    10. repec:zbw:espost:167628 is not listed on IDEAS
    11. Pahlke, Julius & Strasser, Sebastian & Vieider, Ferdinand M., 2012. "Responsibility effects in decision making under risk," Discussion Papers, WZB Junior Research Group Risk and Development SP II 2012-402, Social Science Research Center Berlin (WZB).
    12. Vieider, Ferdinand M. & Chmura, Thorsten & Martinsson, Peter, 2012. "Risk attitudes, development, and growth: Macroeconomic evidence from experiments in 30 countries," Discussion Papers, WZB Junior Research Group Risk and Development SP II 2012-401, Social Science Research Center Berlin (WZB).
    13. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    14. Kaivanto, Kim, 2014. "The effect of decentralized behavioral decision making on system-level risk," MPRA Paper 65972, University Library of Munich, Germany.
    15. repec:kap:theord:v:83:y:2017:i:1:d:10.1007_s11238-016-9585-5 is not listed on IDEAS
    16. Webb, Craig S. & Zank, Horst, 2011. "Accounting for optimism and pessimism in expected utility," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 706-717.
    17. repec:eee:transb:v:102:y:2017:i:c:p:1-21 is not listed on IDEAS
    18. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    19. Julius Pahlke & Sebastian Strasser & Ferdinand Vieider, 2015. "Responsibility effects in decision making under risk," Journal of Risk and Uncertainty, Springer, vol. 51(2), pages 125-146, October.
    20. repec:kap:theord:v:82:y:2017:i:3:d:10.1007_s11238-016-9569-5 is not listed on IDEAS
    21. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier L'Haridon & Author-Name: Chen Li, 2013. "Learning under ambiguity: An experiment using initial public offerings on a stock market," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201331, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    22. Martina Nardon & Paolo Pianca, 2014. "European option pricing with constant relative sensitivity probability weighting function," Working Papers 2014:25, Department of Economics, University of Venice "Ca' Foscari".
    23. Domenico De Giovanni & Fabio Lamantia, 2016. "Control delegation, information and beliefs in evolutionary oligopolies," Journal of Evolutionary Economics, Springer, vol. 26(5), pages 1089-1116, December.

    More about this item

    Keywords

    Curvature; Elevation; Optimism; Pessimism; Preference foundation; Prospect theory;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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