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Iterated expectations under rank‐dependent expected utility and implications for common valuation methods

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  • Alex Stomper
  • Marie‐Louise Vierø

Abstract

This paper investigates the applicability of common valuation techniques in finance when the decision‐maker's preferences can be described by the rank‐dependent expected utility model. Under expected utility theory, compound lotteries can be valued by “iterating” expectations: the expected utility of a compound lottery is the expected value of a simple lottery over prizes that are certainty equivalents to follow‐up lotteries. We derive necessary and sufficient conditions for a similar valuation technique in the framework of rank‐dependent expected utility when a consequentialist decision‐maker has to choose between prospects that belong to a comonotonic class. The conditions coincide with those for dynamically consistent behaviour of such a decision‐maker. The decision‐maker must update her preferences based on a benchmark prospect that can be interpreted as a formalization of “black‐and‐white thinking.” Attentes itératives dans un modèle d'utilité espérée à dépendances de rangs et conséquences pour les méthodes d'évaluation courantes. Cet article analyse l'applicabilité des techniques d'évaluation courantes dans le domaine des finances lorsque les préférences du décideur peuvent être décrites en fonction du modèle d'utilité espérée à dépendances de rangs. Conformément à la théorie d'utilité espérée, les loteries composées peuvent être évaluées selon des attentes « itératives » : l'utilité espérée d'une loterie composée correspond à la valeur espérée d'une loterie simple pour des lots à équivalents garantis lors des loteries à suivre. Nous extrapolons les conditions nécessaires et suffisantes pour une technique d'évaluation semblable dans le cadre du modèle d'utilité espérée à dépendances de rangs lorsqu'un décideur conséquentialiste doit faire un choix entre propositions qui appartiennent à une classe comonotonique. Les conditions coïncident avec celles qui existent pour un comportement dynamique cohérent d'un tel décideur. Le décideur doit mettre ses préférences à jour en fonction d'une proposition de référence pouvant être interprétée comme la formalisation du « raisonnement en noir et blanc ».

Suggested Citation

  • Alex Stomper & Marie‐Louise Vierø, 2022. "Iterated expectations under rank‐dependent expected utility and implications for common valuation methods," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(2), pages 739-763, May.
    • Handle: RePEc:wly:canjec:v:55:y:2022:i:2:p:739-763
    DOI: 10.1111/caje.12593
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    References listed on IDEAS

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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. André Lapied & Pascal Toquebeuf, 2010. "Atemporal non-expected utility preferences, dynamic consistency and consequentialism," Economics Bulletin, AccessEcon, vol. 30(2), pages 1661-1669.
    3. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Siniscalchi, Marciano, 2009. "Two Out Of Three Ain'T Bad: A Comment On “The Ambiguity Aversion Literature: A Critical Assessment”," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 335-356, November.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. Konstantinos Georgalos, 2019. "An experimental test of the predictive power of dynamic ambiguity models," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 51-83, August.
    8. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    9. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    10. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    11. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    12. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    13. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    14. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    15. Alexander Zimper, 2011. "Re-examining the law of iterated expectations for Choquet decision makers," Theory and Decision, Springer, vol. 71(4), pages 669-677, October.
    16. Sebastian Ebert & Philipp Strack, 2015. "Until the Bitter End: On Prospect Theory in a Dynamic Context," American Economic Review, American Economic Association, vol. 105(4), pages 1618-1633, April.
    17. Kliger, Doron & Levy, Ori, 2009. "Theories of choice under risk: Insights from financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 330-346, August.
    18. Dominiak, Adam, 2013. "Iterated Choquet expectations: A possibility result," Economics Letters, Elsevier, vol. 120(2), pages 155-159.
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