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Crisp Fair Gambles

Author

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  • Éric André

    (Aix-Marseille University (Aix-Marseille School of Economics), CNRS & EHESS)

Abstract

Axiomatic models of decision under ambiguity with a non-unique prior allow for the existence of Crisp Fair Gambles: acts whose expected utility is nul whichever of the priors is used. But, in these models, the DM has to be indifferent to the addition of such acts. Their existence is then at odds with a preference taking into account the variance of the prospects. In this paper we study some geometrical and topological properties of the set of priors that would rule out the existence of Crisp Fair Gambles, properties which have consequences on what can be an unambiguous financial asset.

Suggested Citation

  • Éric André, 2014. "Crisp Fair Gambles," AMSE Working Papers 1410, Aix-Marseille School of Economics, Marseille, France, revised 15 Mar 2014.
  • Handle: RePEc:aim:wpaimx:1410
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    References listed on IDEAS

    as
    1. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    2. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 973-982.
    3. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, pages 755-770.
    4. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    5. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    6. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 973-982.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, pages 197-213.
    9. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    10. Cerreia-Vioglio, Simone, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society.
    11. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 341-375.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    14. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, November.
    15. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
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    More about this item

    Keywords

    monotone mean-variance preferences; Ambiguity; set of priors; crisp acts; unambiguous asset;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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