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Variational representation of preferences under ambiguity

Author

Listed:
  • Fabio Maccheroni
  • Massimo Marinacci
  • Aldo Rustichini

Abstract

In the classic Anscombe and Aumann decision setting, we give necessary and sufficient conditions that guarantee the existence of a utility function u on outcomes and an ambiguity index c on the set of all probabilities on the states of the world such that acts are ranked according to the criterion V(f)=min{E(u(f),p)+c(p)} where p ranges over all probability distributions and c is a non-negative convex funcion on the set of all probability distributions. The preferences we characterize include as special cases the multiple priors preferences of Gilboa and Schmeidler, the multiplier preferences of Hansen and Sargent, and the mean-variance preferences of Markowitz and Tobin. In this way we are able to provide a rigorous ambiguity perspective on the latter two models, which have been widely used in macroeconomics and finance.

Suggested Citation

  • Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Variational representation of preferences under ambiguity," ICER Working Papers - Applied Mathematics Series 05-2004, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:05-2004
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    References listed on IDEAS

    as
    1. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
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    Cited by:

    1. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
    2. Youichiro Higashi & Kemal Ozbek & Norio Takeoka, 2025. "Axiomatic Foundations of Bayesian Persuasion," Papers 2512.23409, arXiv.org.
    3. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
    4. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    5. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    6. Ozbek, Kemal, 2023. "Adaptive risk assessments," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    7. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    8. Nascimento, Leandro & Riella, Gil, 2011. "A class of incomplete and ambiguity averse preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 728-750, March.
    9. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    10. Mihm, Maximilian & Ozbek, Kemal, 2018. "Mood-driven choices and self-regulation," Journal of Economic Theory, Elsevier, vol. 176(C), pages 727-760.

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