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 
DOI:  10.1007/s0019900304517 
Contact details of provider:  Web page: http://www.springer.com Web page: http://saet.uiowa.edu/

Order Information:  Web: http://www.springer.com/economics/economic+theory/journal/199/PS2 
References listed on IDEAS
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 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.
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Université Paris1 PanthéonSorbonne (PostPrint and Working Papers)
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 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, J. & Wakker, P.P., 1992.
"The Axiomatic Basis of Anticipated Utility : A Clarification,"
Discussion Paper
19923, Tilburg University, Center for Economic Research.
 Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486499, December.
 Quiggin, J. & Wakker, P., 1992. "The Axiomatic Basis of Anticipated Utility: A Clarification," Papers 9203, Tilburg  Center for Economic Research.
 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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