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

  • Alain Chateauneuf


    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS - UP1 - Université Panthéon-Sorbonne)

  • Michèle Cohen


    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Isaac Meilijson


    (School of Mathematical Sciences [Tel Aviv] - Raymond and Beverly Sackler Faculty of Exact Sciences - Tel Aviv University)

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.

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Date of creation: 2004
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Handle: RePEc:hal:cesptp:halshs-00212281
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  1. Jewitt, Ian, 1987. "Risk Aversion and the Choice between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 73-85, January.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
  7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  8. 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.
  9. 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.
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  11. 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.
  12. 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.
  13. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  14. 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.
  15. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 335-46, July.
  16. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
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