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Uncertainty and Risk in Financial Markets

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Author Info
Luca Rigotti (University of California, Berkeley)
Chris Shannon (University of California, Berkeley)

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Abstract

This paper considers a general equilibrium model in which the distinction between un-certainty and risk is formalized by assuming agents have incomplete preferences over state-contingent consumption bundles, as in Bewley (1986). Without completeness, individual decision making depends on a set of probability distributions over the state space. A bundle is preferred to another if and only if it has larger expected utility for all probabilities in this set. When preferences are complete this set is a singleton, and the model reduces to standard expected utility. In this setting, we characterize Pareto optima and equilibria, and show that the presence of uncertainty generates robust indeterminacies in equilibrium prices and allocations for any specification of initial endowments. We derive comparative statics results linking the degree of uncertainty with changes in equilibria. Despite the presence of robust indeterminacies, we show that equilibrium prices and allocations vary continuously with underlying fundamentals. Equilibria in a standard risk economy are thus robust to adding small degrees of uncertainty. Finally, we give conditions under which some assets are not traded due to uncertainty aversion.

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Paper provided by Department of Economics, Institute for Business and Economic Research, UC Berkeley in its series Department of Economics, Working Paper Series with number 1000.

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Date of creation: 02 Nov 2001
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Handle: RePEc:cdl:econwp:1000

Note: oai:cdlib1:iber/econ-1000
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
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  2. 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. [Downloadable!]
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  3. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March. [Downloadable!] (restricted)
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  5. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July. [Downloadable!] (restricted)
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  6. Hansen, Lars Peter & Sargent, Thomas J & Tallarini, Thomas D, Jr, 1999. "Robust Permanent Income and Pricing," Review of Economic Studies, Blackwell Publishing, vol. 66(4), pages 873-907, October. [Downloadable!] (restricted)
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  7. Tallon, Jean-Marc, 1998. "Asymmetric Information, Nonadditive Expected Utility, and the Information Revealed by Prices: An Example," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 329-42, May.
  8. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March. [Downloadable!] (restricted)
  9. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December. [Downloadable!] (restricted)
  10. Lloyd S. Shapley & Manel Baucells, 1998. "Multiperson Utility," UCLA Economics Working Papers 779, UCLA Department of Economics. [Downloadable!]
  11. Mukerji, Sujoy & Tallon, Jean-Marc, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," Review of Economic Studies, Blackwell Publishing, vol. 68(4), pages 883-904, October.
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  12. Juan Dubra & Fabio Maccheroni & Efe Oki, 2001. "Expected utility theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 11-2001, ICER - International Centre for Economic Research. [Downloadable!]
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  13. Lars Peter Hansen & Thomas J. Sargent, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May. [Downloadable!] (restricted)
  14. Fox, Craig R & Tversky, Amos, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 585-603, August. [Downloadable!] (restricted)
  15. Larry G. Epstein, 2001. "Sharing Ambiguity," American Economic Review, American Economic Association, vol. 91(2), pages 45-50, May. [Downloadable!] (restricted)
  16. Heath, Chip & Tversky, Amos, 1991. " Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
  17. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December. [Downloadable!] (restricted)
  18. Samuelson, William & Zeckhauser, Richard, 1988. " Status Quo Bias in Decision Making," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 7-59, March.
  19. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January. [Downloadable!] (restricted)
  20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Atsushi Kajii & Takashi Ui, 2007. "Interim Efficient Allocations under Uncertainty," Working Papers 642, Kyoto University, Institute of Economic Research. [Downloadable!]
  2. B. Douglas Bernheim & Antonio Rangel, 2008. "Beyond Revealed Preference: Choice Theoretic Foundations for Behavioral Welfare Economics," NBER Working Papers 13737, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Eric Danan & Anthony Ziegelmeyer, 2004. "Are preferences incomplete? An experimental study using flexible choices," Discussion Papers on Strategic Interaction 2004-23, Max Planck Institute of Economics, Strategic Interaction Group. [Downloadable!]
  4. Eric Danan & Anthony Ziegelmeyer, 2006. "Are preferences complete? An experimental measurement of indecisiveness under risk," Discussion Papers on Strategic Interaction 2006-01, Max Planck Institute of Economics, Strategic Interaction Group. [Downloadable!]
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