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Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model

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Author Info
Alain Chateauneuf () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I)
Michèle Cohen () (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - CNRS : UMR8594 - Université Panthéon-Sorbonne - Paris I)
Isaac Meilijson () (School of mathematical science - Tel Aviv University)

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Abstract

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00212281_v1.

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Date of creation: 2004
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Publication status: Published, Journal of Mathematical Economics, 2004, 40, 547-571
Handle: RePEc:hal:cesptp:halshs-00212281_v1

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Related research
Keywords: Location-independent risk; monotone increase in risk; rank-dependent expected utility.;

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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.:
  1. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Blackwell Publishing, vol. 36(107), pages 335-46, July. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September. [Downloadable!] (restricted)
  12. Jewitt, Ian, 1987. "Risk Aversion and the Choice between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Blackwell Publishing, vol. 54(1), pages 73-85, January. [Downloadable!] (restricted)
  13. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Frank A Cowell, 2007. "Income Distribution and Inequality," STICERD - Distributional Analysis Research Programme Papers 94, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. Alain Chateauneuf & Patrick Moyes, 2004. "Lorenz Non-Consistent Welfare and Inequality Measurement," IDEP Working Papers 0406, Institut d'economie publique (IDEP), Marseille, France, revised May 2004. [Downloadable!]
    Other versions:
  3. Zank, Horst & Schmidt, Ulrich & Diecidue, Enrico, 2007. "Parametric Weighting Functions," Economics Working Papers 2007,01, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
    Other versions:
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