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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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  • Alain Chateauneuf

    ()

  • Michéle Cohen

    ()

  • Isaac Meilijson

    ()

Abstract

This paper studies monotone risk aversion, the aversion to monotone, mean-preserving 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 and 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 G u of the utility function u and an index of pessimism P f of the probability perception function f: the decision maker is monotone risk averse if and only if $P_f\ge G_u$ . The index of greediness (non-concavity) of u is the supremum of $u^{\prime}(x)/u^{\prime}(y)$ taken over $y\leq x$ . The index of pessimism of f is the infimum of ${\frac{{1-f(v)}}{{1-v}}}/ {\frac{{f(v)}}{{v}}}$ taken over 0 > v > 1. Thus, $G_{u}\geq 1$ , with G u =1 iff u is concave. If $P_{f}\geq G_{u}$ then $P_{f}\geq 1$ , i.e., f is majorized by the identity function. Since P f =1 for Expected Utility maximizers, $P_{f}\geq G_{u}$ forces u to be concave in this case; thus, the characterization of risk aversion as $P_{f}\geq G_{u}$ is a direct generalization from EU to RDEU. A novel element is that concavity of u is not necessary. In fact, u must be concave only if P f =1. Copyright Springer-Verlag Berlin/Heidelberg 2005

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 25 (2005)
Issue (Month): 3 (04)
Pages: 649-667

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Handle: RePEc:spr:joecth:v:25:y:2005:i:3:p:649-667

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Keywords: Risk aversion; Pessimism; Greediness; Rank-dependent expected utility.;

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  1. Quiggin, J. & Wakker, P., 1992. "The Axiomatic Basis of Anticipated Utility: A Clarification," Papers 9203, Tilburg - Center for Economic Research.
  2. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
  3. Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2004. "Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00212281, HAL.
  4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
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