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

## Abstract

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## Download Info

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.

## Bibliographic Info

Article provided by Springer in its journal Economic Theory.
**Volume (Year):** 25 (2005)

**Issue (Month):** 3 (04)

**Pages:** 649-667

**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

## Related research

**Keywords:**Risk aversion; Pessimism; Greediness; Rank-dependent expected utility.;

**Other versions of this item:**

- Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997.
"
**More Pessimism than Greediness: A Characterization of Monotone Risk Aversion in the Rank-Dependant Expected Utility Model**," Papiers d'Economie MathÃÂ©matique et Applications 97.53, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).

**Find related papers by JEL classification:**

**D81**- Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty**C60**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

## References

**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.:

- Quiggin, J. & Wakker, P., 1992.
"
**The Axiomatic Basis of Anticipated Utility: A Clarification**," Papers 9203, Tilburg - 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 486-499, December.

- Quiggin, J. & Wakker, P., 1992.
"
**The Axiomatic Basis of Anticipated Utility : A Clarification**," Discussion Paper 1992-3, Tilburg University, Center for Economic Research.

- Quiggin John & Wakker Peter, 1994.
"
- 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. - Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004.
"
**Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model**," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.

- Yaari, Menahem E, 1987.
"
**The Dual Theory of Choice under Risk**," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. - Quiggin, John, 1982.
"
**A theory of anticipated utility**," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.

**Full references**(including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.**Cited by:**

**This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.**

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.## Statistics

Access and download statistics## Corrections

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.