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

Michèle Cohen () and Isaac Meilijson ()
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Isaac Meilijson: School of Mathematical Sciences - Tel Aviv University, http://www.math.tau.ac.il/~isaco/

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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 ? (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

Keywords: Choquet Utility; greediness; pessimism; Rank-dependent Utility; Risk aversion uncertainty (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-upt
Date: 2011-05
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