IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

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

  • Alain Chateauneuf

    ()

  • Michéle Cohen

    ()

  • Isaac Meilijson

    ()

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 $P_f\ge G_u$ . The index of greediness (non-concavity) 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 ${\frac{{1-f(v)}}{{1-v}}}/ {\frac{{f(v)}}{{v}}}$ 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 Springer-Verlag 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.

File URL: http://hdl.handle.net/10.1007/s00199-003-0451-7
Download Restriction: Access to full text is restricted to subscribers.

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.

Article provided by Springer in its journal Economic Theory.

Volume (Year): 25 (2005)
Issue (Month): 3 (04)
Pages: 649-667

as
in new window

Handle: RePEc:spr:joecth:v:25:y:2005:i:3:p:649-667
Contact details of provider: Web page: http://link.springer.de/link/service/journals/00199/index.htm

Order Information: Web: http://link.springer.de/orders.htm

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.:

as in new window
  1. Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2004. "Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00212281, HAL.
  2. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
  3. Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486-499, December.
  4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
Full references (including those not matched with items on IDEAS)

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:649-667. 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: (Guenther Eichhorn)

or (Christopher F Baum)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.