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
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
 Miles S. Kimball, 1989.
"Precautionary Saving in the Small and in the Large,"
NBER Working Papers
2848, National Bureau of Economic Research, Inc.
 Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 5373, January.
 Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323343, December.
 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, J. & Wakker, P.P., 1992. "The Axiomatic Basis of Anticipated Utility : A Clarification," Discussion Paper 19923, Tilburg University, Center for Economic Research.
 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.
 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.
 Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95115, January.
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.
When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:25:y:2005:i:3:p:649667. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)
or (Rebekah McClure)If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.