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

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Author Info
Alain Chateauneuf () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I)
Michèle Cohen () (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - CNRS : UMR8594 - Université Panthéon-Sorbonne - Paris I)
Isaac Meilijson () (School of mathematical science - Tel Aviv University)

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Abstract

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 twofunctions, 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 onlyif Pf exceeds Gu. A novel element is that concavity of u is not necessary. In fact, u must be concave only if Pf = 1.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00211906_v1.

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Date of creation: 2005
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Publication status: Published, Economic Theory, 2005, 25, 649-667
Handle: RePEc:hal:cesptp:halshs-00211906_v1

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Related research
Keywords: Risk aversion; pessimism; greediness; Rank-dependent Expected Utility;

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References listed on IDEAS
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  1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
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  1. Grant, S. & Quiggin, J., 2001. "A model-free definition of increasing uncertainty," Discussion Paper 84, Tilburg University, Center for Economic Research. [Downloadable!]
  2. Jürgen Eichberger & David Kelsey, 2007. "Ambiguity," Working Papers 0448, University of Heidelberg, Department of Economics, revised Jul 2007. [Downloadable!]
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  3. Jordi Caballe & Joan Ma. Esteban, 2002. "Stochastic Dominance and Absolute Risk Aversion," UFAE and IAE Working Papers 506.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
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