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Risk, ambiguity, and the separation of utility and beliefs

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  • Massimo Marinacci

    ()

  • Paolo Ghirardato

    ()

Abstract

We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization. Elsewhere (forthcoming) we show that it can be very helpful in the characterization of a notion of ambiguity aversion, as separating utility and beliefs allows to identify and remove aspects of risk attitude from the decision maker’s behavior. Here we show that the model allows to generalize several results on the characterization of risk aversion in betting behavior. These generalizations are of independent interest, as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts.

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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 21-2001.

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Length: 38 pages
Date of creation: Jul 2001
Date of revision:
Handle: RePEc:icr:wpmath:21-2001

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  1. 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.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  3. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
  4. 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.
  5. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001. "A Subjective Spin on Roulette Wheels," Working Papers 1127, California Institute of Technology, Division of the Humanities and Social Sciences.
  6. Gerard Debreu & Tjalling C. Koopmans, 1980. "Additively Decomposed Quasiconvex Functions," Cowles Foundation Discussion Papers 574, Cowles Foundation for Research in Economics, Yale University.
  7. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  9. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-69, January.
  10. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  11. Luigi Montrucchio & Fabio Privileggi, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," ICER Working Papers - Applied Mathematics Series 05-2001, ICER - International Centre for Economic Research.
  12. 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.
  13. 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.
  14. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  15. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  16. 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.
  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. 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).
  19. 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.
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