TY - JOUR

T1 - More pessimism than greediness

T2 - A characterization of monotone risk aversion in the rank-dependent expected utility model

AU - Chateauneuf, Alain

AU - Cohen, Michéle

AU - Meilijson, Isaac

PY - 2005/4

Y1 - 2005/4

N2 - 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 Pf ≥ G u. The index of greediness (non-concavity) of u is the supremum of u′(x)/u′(y) taken over y ≤ x. The index of pessimism of f is the infimum of 1-f(v)/1-v/f(v)/v taken over 0 < v < 1. Thus, Gu ≥ 1, with Gu = 1 iff u is concave. If Pf ≥ G u then Pf ≥ 1, i.e., f is majorized by the identity function. Since P f = 1 for Expected Utility maximizers, P f ≥ Gu forces u to be concave in this case; thus, the characterization of risk aversion as Pf ≥ Gu 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.

AB - 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 Pf ≥ G u. The index of greediness (non-concavity) of u is the supremum of u′(x)/u′(y) taken over y ≤ x. The index of pessimism of f is the infimum of 1-f(v)/1-v/f(v)/v taken over 0 < v < 1. Thus, Gu ≥ 1, with Gu = 1 iff u is concave. If Pf ≥ G u then Pf ≥ 1, i.e., f is majorized by the identity function. Since P f = 1 for Expected Utility maximizers, P f ≥ Gu forces u to be concave in this case; thus, the characterization of risk aversion as Pf ≥ Gu 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.

KW - Greediness

KW - Pessimism

KW - Rank-dependent expected utility

KW - Risk aversion

UR - http://www.scopus.com/inward/record.url?scp=12344267557&partnerID=8YFLogxK

U2 - 10.1007/s00199-003-0451-7

DO - 10.1007/s00199-003-0451-7

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AN - SCOPUS:12344267557

SN - 0938-2259

VL - 25

SP - 649

EP - 667

JO - Economic Theory

JF - Economic Theory

IS - 3

ER -