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Ambiguity in the small and in the large

Author

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  • Paolo Ghirardato
  • Marciano Siniscalchi

Abstract

This paper considers local and global multiple-prior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, i.e. admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either Certainty Independence or Uncertainty Aversion. We show that the set of priors identified by Ghirardato, Maccheroni, and Marinacci (2004)’s ‘unambiguous preference’ relation can be characterized as a union of Clarke differentials. We then introduce a behavioral notion of ‘locally better deviation’ at an act, and show that it characterizes the Clarke differential of the preference representation at that act. These results suggest that the priors identified by these preference statements are directly related to (local) optimizing behavior.

Suggested Citation

  • Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the small and in the large," Carlo Alberto Notebooks 255, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:255
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    Cited by:

    1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "On the equality of Clarke-Rockafellar and Greenberg-Pierskalla differentials for monotone and quasiconcave functionals," Working Papers 561, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Rustichini, A., 2015. "The structure of variational preferences," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 12-19.
    3. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications, Elsevier.
    4. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    5. Kopylov, Igor, 2016. "Canonical utility functions and continuous preference extensions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 32-37.
    6. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    7. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Econometrica, Econometric Society, vol. 82, pages 1945-1978, September.
    8. Daniele Pennesi, 2013. "Endogenous Status Quo," Carlo Alberto Notebooks 314, Collegio Carlo Alberto.
    9. André, Eric, 2016. "Crisp monetary acts in multiple-priors models of decision under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 153-161.
    10. Huang, Yi-Chieh & Tzeng, Larry Y. & Zhao, Lin, 2015. "Comparative ambiguity aversion and downside ambiguity aversion," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 257-269.
    11. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Stochastic Dominance Analysis without the Independence Axiom," Working Papers 549, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
    13. repec:eee:jetheo:v:173:y:2018:i:c:p:257-288 is not listed on IDEAS

    More about this item

    Keywords

    Ambiguity; Optimization; Robustness; Derivative.;

    JEL classification:

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

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