In search of characterization of the preference for safety under the Choquet model
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.
|Date of creation:||May 2011|
|Publication status:||Published in Documents de travail du Centre d'Economie de la Sorbonne 2011.31 - ISSN : 1955-611X. 2011|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00594082|
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- Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005.
"More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, 04.
- Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997. "More Pessimism than Greediness: A Characterization of Monotone Risk Aversion in the Rank-Dependant Expected Utility Model," Papiers d'Economie MathÃ©matique et Applications 97.53, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00211906, HAL.
- Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
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