In search of a characterization of the preference for safety under the Choquet model
AbstractVictor 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 ? (v and ?) be Ursula's (Victor's) utility and capacity. A necessary and sufficient condition (A) on the pairs (u, ?) and (v, ?) 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 ? (.) = f (? (.))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.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 11031.
Length: 21 pages
Date of creation: May 2011
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Choquet Utility; greediness; pessimism; Rank-dependent Utility; Risk aversion uncertainty.;
Other versions of this item:
- Michèle Cohen & Isaac Meilijson, 2011. "In search of characterization of the preference for safety under the Choquet model," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00594082, HAL.
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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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, 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 MathÃÂ©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," UniversitÃ© Paris1 PanthÃ©on-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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