More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model

Alain Chateauneuf, Michèle Cohen and Isaac Meilijson ()

Economic Theory, 2005, vol. 25, issue 3, 649-667

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

Keywords: Risk aversion; Pessimism; Greediness; Rank-dependent expected utility. (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (51)

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Related works:
Working Paper: More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model (2005)
Working Paper: More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model (2005)
Working Paper: More Pessimism than Greediness: A Characterization of Monotone Risk Aversion in the Rank-Dependant Expected Utility Model (1997)
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DOI: 10.1007/s00199-003-0451-7

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