More pessimism than greediness: a characterization of monotone risk aversion in the rankdependent expected utility model
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 probabilityperception function f. Monotone meanpreserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel and Lehmann [3,4] in Nonparametric 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 (nonconcavity) 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 ${\frac{{1f(v)}}{{1v}}}/ {\frac{{f(v)}}{{v}}}$ 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 SpringerVerlag Berlin/Heidelberg 2005
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Volume (Year): 25 (2005)
Issue (Month): 3 (04)
Pages: 649667
Handle:  RePEc:spr:joecth:v:25:y:2005:i:3:p:649667 
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 Quiggin John & Wakker Peter, 1994.
"The Axiomatic Basis of Anticipated Utility: A Clarification,"
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 Quiggin, J. & Wakker, P., 1992. "The Axiomatic Basis of Anticipated Utility: A Clarification," Papers 9203, Tilburg  Center for Economic Research.
 Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95115, January.
 Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2004.
"Four notions of mean preserving increase in risk, risk attitudes and applications to the RankDependent Expected Utility model,"
Université Paris1 PanthéonSorbonne (PostPrint and Working Papers)
halshs00212281, HAL.
 Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of meanpreserving increase in risk, risk attitudes and applications to the rankdependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547571, August.
 Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323343, December.
 Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Nonexpected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 7791, July.
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