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Allais, Ellsberg, and Preferences for Hedging

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  • Mark Dean
  • Pietro Ortoleva

Abstract

We study the relation between ambiguity aversion and the Allais paradox. To this end, we introduce a novel de nition of hedging which applies to objective lotteries as well as to uncertain acts, and we use it to de ne a novel axiom that captures a preference for hedging which generalizes the one of Schmeidler (1989). We argue how this generalized axiom captures both aversion to ambiguity, and attraction towards certainty for objective lotteries. We show that this axiom, together with other standard ones, is equivalent to to two representations both of which generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both, the agent reacts to ambiguity using multiple priors, but does not use expected utility to evaluate objective lotteries. In our rst representation, the agent treats objective lotteries as `ambiguous objects,' and use a set of priors to evaluate them. In the second, equivalent representation, lotteries are evaluated by distorting probabilities as in the Rank-Dependent Utility model, but using the worst from a set of such distortions. Finally, we show how a preference for hedging is not sucient to guarantee an Ellsberg-like behavior if the agent violate expected utility for objective lotteries. We then provide an axiom that guarantees that this is the case, and nd an associated representation in which the agent rst maps acts to an objective lottery using the worst of the priors in a set; then evaluates this lottery using the worst distortion from a set of concave Rank-Dependent Utility functionals.

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File URL: http://www.brown.edu/Departments/Economics/Papers/2012/2012-2_paper.pdf
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Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2012-2.

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Date of creation: 2012
Date of revision:
Handle: RePEc:bro:econwp:2012-2

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Postal: Department of Economics, Brown University, Providence, RI 02912

Related research

Keywords: Ambiguity Aversion; Allais Paradox; Ellsberg Paradox; Hedging; Multiple Priors; Subjective Mixture; Probability Weighting; Rank Dependent Expected Utility;

This paper has been announced in the following NEP Reports:

References

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  1. Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & Jean-Marc Tallon, 2003. "Monotone Continuous Multiple Priors," ICER Working Papers - Applied Mathematics Series 30-2003, ICER - International Centre for Economic Research.
  2. Yoram Halevy & Vincent Feltkamp, . "A Bayesian Approach to Uncentainty Aversion," CARESS Working Papres 99-03, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  3. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  4. Dillenberger, David, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," MPRA Paper 8342, University Library of Munich, Germany.
  5. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, 03.
  6. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer, vol. 48(2), pages 341-375, October.
  7. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, 07.
  8. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  9. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
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Citations

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Cited by:
  1. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva, 2014. "Cautious Expected Utility and the Certainty Effect," PIER Working Paper Archive 14-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2011. "Optimism and Pessimism with Expected Utility, Third Version," PIER Working Paper Archive 13-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 26 Dec 2012.
  3. David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2011. "Optimism and Pessimism with Expected Utility, Fourth Version," PIER Working Paper Archive 13-068, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Nov 2013.

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