Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model
This article presents various notions of risk generated by the intuitively appealing single-crossing operations between distribution functions. These stochastic orders, Bickel & Lehmann dispersion or (its equal-mean version) Quiggin's monotone mean-preserving increase in risk and Jewitt's location-independent risk, have proved to be useful in the study of Pareto allocations, ordering of insurance premia and other applications in the Expected Utility setup. These notions of risk are also relevant tothe Quiggin-Yaari Rank-dependent Expected Utility (RDEU) model of choice among lotteries. Risk aversion is modeled in the vNM Expected Utility model by Rothschild & Stiglitz's Mean Preserving Increase in Risk (MPIR). Realizing that in the broader rank-dependent set-up this order is too weak to classify choice, Quiggin developed the stronger monotone MPIR for this purpose. This paper reviews four notions of mean-preserving increase in risk - MPIR, monotoneMPIR and two versions of location-independent risk (renamed here left and right monotone MPIR) - and shows which choice questions are consistently modeled by each of these four orders.
|Date of creation:||2004|
|Date of revision:|
|Publication status:||Published in Journal of Mathematical Economics, Elsevier, 2004, 40, pp.547-571. <10.1016/S0304-4068(03)00044-2>|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00212281|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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.:
- Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-38, May.
- Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
- G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
- Christian Gollier & Harris Schlesinger, 1996.
"Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*),"
Springer, vol. 7(2), pages 359-363.
- Gollier, Christian & Schlesinger, Harris, 1996. "Arrow's Theorem on the Optimality of Deductibles: A Stochastic Dominance Approach," Economic Theory, Springer, vol. 7(2), pages 359-63, February.
- Karni, Edi & Schwartz, Aba, 1977. "Search theory: The case of search with uncertain recall," Journal of Economic Theory, Elsevier, vol. 16(1), pages 38-52, October.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
- Chateauneuf, Alain, 1991. "On the use of capacities in modeling uncertainty aversion and risk aversion," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 343-369.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005.
"More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model,"
Springer, vol. 25(3), pages 649-667, 04.
- Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00211906, HAL.
- 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 MathÃ©matique et Applications 97.53, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Mich�le D. Cohen, 1995. "Risk-Aversion Concepts in Expected- and Non-Expected-Utility Models," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 20(1), pages 73-91, June.
- Menahem E. Yaari, 1984. "Risk Aversion Without Diminishing Marginal Utility," STICERD - Theoretical Economics Paper Series 106, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
- Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-27, March.
- Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 73-85.
- Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
- Landsberger, Michael & Meilijson, Isaac, 1990. "Demand for risky financial assets: A portfolio analysis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 204-213, February.
- Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
- Moyes Patrick, 1994. "Inequality Reducing and Inequality Preserving Transformations of Incomes: Symmetric and Individualistic Transformations," Journal of Economic Theory, Elsevier, vol. 63(2), pages 271-298, August.
When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00212281. 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: (CCSD)
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.