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Risk, Ambiguity and the Separation of Utility and Beliefs

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  • Paolo Ghirardato

    (California Institute of Technology)

  • Massimo Marinacci

    (Universita di Bologna)

Abstract

The theory of subjective expected utility (SEU) has been extended in many recent works, allowing ambiguity to matter for choice. However, a fully satisfactory and general notion of ambiguity aversion, analogous to risk aversion for SEU, is still missing. Using a new preference model which encompasses most of the recent literature, we provide such a definition by building on a comparative notion of ambiguity aversion. The development of the latter is not immediate, since it is necessary to distinguish between differences in ambiguity and risk attitude. The solution offered here is very general as it only requires a richness condition on the set of consequences. Employing the comparative notion, we call `ambiguity averse' a preference relation which is `more ambiguity averse' than a SEU preference with similar risk attitude. We show that ambiguity aversion in this sense has a simple characterization, especially for the specific models that are most popular in the literature. We next build on these ideas to provide a definition of unambiguous act and event. We show that for preferences which have a consistent ambiguity attitude, the sets of these acts and events have a simple and easily checked characterization. As an illustration, we consider the classical Ellsberg 3-color urn problem and find that the notions developed in the paper provide the intuitive answers.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1143.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1143

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  1. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
  2. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  3. 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.
  4. Tallon, J.-M. & Chateauneuf, A., 1998. "Diversification, Convex Preferences and Non-Empty Core," Papiers d'Economie Mathématique et Applications 98.32, Université Panthéon-Sorbonne (Paris 1).
  5. Gerard Debreu & Tjalling C. Koopmans, 1980. "Additively Decomposed Quasiconvex Functions," Cowles Foundation Discussion Papers 574, Cowles Foundation for Research in Economics, Yale University.
  6. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  8. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers - Applied Mathematics Series 17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
  10. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," POLIS Working Papers 5, Institute of Public Policy and Public Choice - POLIS.
  11. Ghirardato, Paolo & Marinacci, Massimo, 2000. "Range Convexity and Ambiguity Averse Preferences," Working Papers 1081, California Institute of Technology, Division of the Humanities and Social Sciences.
  12. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  14. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May.
  15. Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469-479, April.
  16. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  17. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
  18. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  19. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-69, January.
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