The measure representation: A correction

Segal, Uzi

doi:10.1007/bf01065353

Cited by 39 publications

(14 citation statements)

References 5 publications

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“…Also, this new alternative characterization is incorrect, as will be shown by the examples below. A correct theorem that avoids the problems indicated in this article will appear in Segal (1992). Correct results have also appeared in Chateauneuf (1990) and Chew and Wakker (1991, section 5).…”

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confidence: 52%

Counterexamples to Segal's measure representation theorem

Wakker

1993

J Risk Uncertainty

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confidence: 52%

Counterexamples to Segal's measure representation theorem

Wakker

1993

J Risk Uncertainty

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“…Variants of the Rank Dependent Expected Utility theory due to Quiggin [20] have been treated by Yaari [32], Chew, Karni & Safra [11], Segal [28,29] and Allais [2]. General axiomatization can be found in Wakker [30], Quiggin & Wakker [22], Chateauneuf [6].…”

Section: The Rdeu Modelmentioning

confidence: 99%

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

2005

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To cite this version:Alain Chateauneuf, Michèle Cohen, Isaac Meilijson. More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model. Economic Theory, Springer Verlag, 2005, 25, pp.649-667. 10.1007 More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model Summary. 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 probability-perception function f . Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel & 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¸Gu . The index of greediness (non-concavity) of u is the supremum of u 0 (x)=u 0 (y) taken over y · x. The index of pessimism of f is the in¯mum ofv taken over 0 < v < 1. Thus, G u¸1 , with G u = 1 i® u is concave. If P f¸Gu then P f¸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 P f¸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.

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“…He suggested to evaluate the distribution functions of real-valued random variables by a measure defined over their epigraphs and dubbed this as the "measure representation" approach. A few papers followed in this vein until Wakker (1993) pointed out an error in the statement of the representation theorem, which was amended in Segal (1993). Subsequently, a few papers have extended the measure representation approach to different environments.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking real-valued acts

Castagnoli¹,

LiCalzi²

2006

Games and Economic Behavior

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A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark β which may itself be a random variable; that is, an act f is evaluated by means of the functional V (f ) = P (f β). Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P .

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The measure representation: A correction

Cited by 39 publications

References 5 publications

Counterexamples to Segal's measure representation theorem

Counterexamples to Segal's measure representation theorem

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

Benchmarking real-valued acts

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