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Unbounded probabilistic sophistication

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  • Kopylov, Igor

Abstract

I extend Machina and Schmeidler's (1992) model of probabilistic sophistication to unbounded uncertain prospects (acts) and derive risk preferences over the induced probability distributions (lotteries) with unbounded support. For example, risk preferences can be derived over normal, exponential, and Poisson families of probability distributions. My extension uses a version of Arrow's (1970) Monotone Continuity, which implies countable additivity for subjective beliefs and a novel property of tail-continuity for the revealed risk preferences. On the other hand, I do not assume P6 (Small Event Continuity) that is used both by Savage (1954) and Machina-Schmeidler.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 60 (2010)
Issue (Month): 2 (September)
Pages: 113-118

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Handle: RePEc:eee:matsoc:v:60:y:2010:i:2:p:113-118

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Probabilistic sophistication Countable additivity Monotone continuity Tail continuity;

References

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  1. Massimo Marinacci, 2001. "Probabilistic sophistication and multiple priors," ICER Working Papers - Applied Mathematics Series 08-2001, ICER - International Centre for Economic Research.
  2. repec:hal:cesptp:halshs-00177057 is not listed on IDEAS
  3. 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.
  4. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  5. Wakker, Peter, 1993. "Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 487-93, April.
  6. Chew Soo Hong & Jacob S. Sagi, 2006. "Event Exchangeability: Probabilistic Sophistication Without Continuity or Monotonicity," Econometrica, Econometric Society, vol. 74(3), pages 771-786, 05.
  7. Sarin, Rakesh & Wakker, Peter P., 2000. "Cumulative dominance and probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 191-196, September.
  8. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
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