IDEAS home Printed from https://ideas.repec.org/p/ags/quedwp/273724.html

Iterated Expectations under Rank-Dependent Expected Utility and Model Consistency

Author

Listed:
  • Stomper, Alex
  • VierAy, Marie-Louise

Abstract

Under expected utility theory, compound lotteries can be valued by \iterating" expecta- tions: 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 suffcient conditions for a similar valuation technique in the framework of rank-dependent expected utility (RDU) when a decision maker has to choose between prospects that belong to a comonotonic class and his preferences satisfy consequentialism. The conditions are so restrictive that they can be viewed as an impossibility result. Our contribution thus identifies a challenge for future research. If we accept RDU as the model of behavior, we either need to find alternative valuation algorithms, or we need to relax the assumption of preference exogeneity.

Suggested Citation

  • Stomper, Alex & VierAy, Marie-Louise, 2015. "Iterated Expectations under Rank-Dependent Expected Utility and Model Consistency," Queen's Economics Department Working Papers 273724, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:273724
    DOI: 10.22004/ag.econ.273724
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/273724/files/qed_wp_1228.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.273724?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    5. 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.
    6. 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.
    7. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    8. 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.
    9. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    10. Dominiak, Adam, 2013. "Iterated Choquet expectations: A possibility result," Economics Letters, Elsevier, vol. 120(2), pages 155-159.
    11. 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.
    12. 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.
    13. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    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. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    16. 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.
    17. 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..
    18. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    3. André Lapied & Robert Kast, 2005. "Updating Choquet valuation and discounting information arrivals," Working Papers 05-09, LAMETA, Universtiy of Montpellier, revised Jan 2005.
    4. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    5. Border, Kim C. & Segal, Uzi, 1997. "Coherent Odds and Subjective Probability," University of Western Ontario, Departmental Research Report Series 9717, University of Western Ontario, Department of Economics.
    6. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
    7. repec:rza:wpaper:240 is not listed on IDEAS
    8. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    9. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    10. André Lapied & Pascal Toquebeuf, 2011. "Dynamically consistent CEU preferences," Working Papers halshs-00856193, HAL.
    11. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    12. 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.
    13. Rawley Heimer & Zwetelina Iliewa & Alex Imas & Martin Weber, 2025. "Dynamic Inconsistency in Risky Choice: Evidence from the Lab and Field," American Economic Review, American Economic Association, vol. 115(1), pages 330-363, January.
    14. Nobuo Koida, 2012. "Nest-monotonic two-stage acts and exponential probability capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 99-124, May.
    15. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. Hagen Lindstädt, 2004. "Entscheidungskalküle jenseits des subjektiven Erwartungsnutzens," Schmalenbach Journal of Business Research, Springer, vol. 56(6), pages 495-519, September.
    17. Alex Stomper & Marie-Louise Vierø, 2015. "Iterated Expectations Under Rank-dependent Expected Utility And Model Consistency," Working Paper 1228, Economics Department, Queen's University.
    18. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    19. Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    20. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    21. Bleichrodt, Han & Eichberger, Jürgen & Grant, Simon & Kelsey, David & Li, Chen, 2021. "Testing dynamic consistency and consequentialism under ambiguity," European Economic Review, Elsevier, vol. 134(C).

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ags:quedwp:273724. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/qedquca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.