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Riskiness for sets of gambles

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  • Moti Michaeli

Abstract

Aumann--Serrano (2008) and Foster--Hart (2009) suggest two new riskiness measures, each of which enables one to elicit a complete and objective ranking of gambles according to their riskiness. Hart (2011) shows that both measures can be obtained by looking at a large set of utility functions and applying "uniform rejection criteria" to rank the gambles in accordance with this set of utilities. We use the same "uniform rejection criteria" to extend these two riskiness measures to the realm of uncertainty and develop complete and objective rankings of sets of gambles, which arise naturally in models of decision making under uncertainty.

Suggested Citation

  • Moti Michaeli, 2012. "Riskiness for sets of gambles," Discussion Paper Series dp603, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp603
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    References listed on IDEAS

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    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
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    3. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    4. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    5. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    6. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    7. Jurgen Eichberger & Simon Grant & David Kelsey & Gleb A. Koshevoy, 2009. "The a-MEU Model: A Comment," Discussion Papers 0903, Exeter University, Department of Economics.
    8. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    9. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
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    11. Amnon Schreiber, 2012. "An Economic Index of Relative Riskiness," Discussion Paper Series dp597, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    12. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    13. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
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    16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    Cited by:

    1. Hart, Sergiu & Foster, Dean P., 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society, vol. 8(2), May.
    2. Amnon Schreiber, 2014. "Economic indices of absolute and relative riskiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 309-331, June.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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