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In search of characterization of the preference for safety under the Choquet model

Author

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  • Michèle Cohen

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

  • Isaac Meilijson

    () (School of Mathematical Sciences [Tel Aviv] - Raymond and Beverly Sackler Faculty of Exact Sciences - Tel Aviv University [Tel Aviv])

Abstract

Victor prefers safety more than Ursula if whenever Ursula prefers some constant to some uncertain act, so does Victor. This paradigm, whose Expected Utility version takes the form of Arrow & Pratt's more risk averse concept, will be studied in the Choquet Uncertainty model, letting u and μ (v and ν) be Ursula's (Victor's) utility and capacity. A necessary and sufficient condition (A) on the pairs (u, μ) and (v, ν) will be presented for dichotomous weak increased uncertainty aversion, the preference by Victor of a constant over a dichotomous act whenever such is the preference of Ursula. This condition, pointwise inequality between a function defined in terms of v (u-1(⋅)) and another defined purely in terms of the capacities, preserves the flavor of the "more pessimism than greediness" characterization of monotone risk aversion by Chateauneuf, Cohen & Meilijson in the Rank-dependent Utility Model and its extension by Grant & Quiggin to the Choquet Utility Model. A sufficient condition (B) in terms of the capacities only, satisfied in particular if ν (⋅) = f (μ (⋅)) for some convex f, will be presented for more simplicity seeking, the preference by Victor over any act for some dichotomous act, that leaves Ursula indifferent. Condition A is thus a characterization of weak increased uncertainty aversion for convex f. An example will be exhibited disproving the more far reaching conjecture under which the dichotomous case implies the general case.

Suggested Citation

  • Michèle Cohen & Isaac Meilijson, 2011. "In search of characterization of the preference for safety under the Choquet model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00594082, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00594082
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00594082
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    References listed on IDEAS

    as
    1. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    2. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
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    Keywords

    Modèle de Choquet; avidité; pessimisme; utilité dépendant du rang; aversion pour le risque; incertain.; Choquet Utility; greediness; pessimism; Rank-dependent Utility; Risk aversion; uncertainty.;

    JEL classification:

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

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