More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model

Alain Chateauneuf (1) , Michèle Cohen (2) , Isaac Meilijson (3)

1 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique
2 EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative
3 TAU - School of Mathematical Sciences [Tel Aviv]

This paper studies monotone risk aversion, the aversion to monotone, meanpreserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by two
functions, a utility function u in conjunction with a probability-perception function f.
Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel & Lehmann [3, 4] in Non-parametric Statistics. We present a characterization of the pairs (u; f) of monotone risk averse decision makers, based on an index of greediness Gu of the utility function u and an index of pessimism Pf of the probability perception function f: the decision maker is monotone risk averse if and only
if Pf exceeds Gu. A novel element is that concavity of u is not necessary. In fact, u must be concave only if Pf = 1.

Mots clés: Risk aversion; pessimism; greediness; Rank-dependent Expected Utility

Domaines: Economies et finances

Alain Chateauneuf, Michèle Cohen, Isaac Meilijson. More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model. Economic Theory, 2005, 25, pp.649-667. ⟨10.1007/s00199-003-0451-7⟩. ⟨halshs-00211906⟩