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Stochastic Dominance and Absolute Risk Aversion

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  • Jordi Caballé
  • Joan-Maria Esteban

Abstract

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Suggested Citation

  • Jordi Caballé & Joan-Maria Esteban, 2003. "Stochastic Dominance and Absolute Risk Aversion," Working Papers 9, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:9
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    References listed on IDEAS

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    1. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    2. 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.
    3. Lambert, Peter J. & Hey, John D., 1979. "Attitudes to risk," Economics Letters, Elsevier, vol. 2(3), pages 215-218.
    4. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    5. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    6. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    7. Christian Gollier & Miles S. Kimball, 2018. "New methods in the classical economics of uncertainty: comparing risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 5-23, May.
    8. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    9. Meyer, Jack, 1977. "Second Degree Stochastic Dominance with Respect to a Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 477-487, June.
    10. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    11. Meyer, Jack, 1975. "Increasing risk," Journal of Economic Theory, Elsevier, vol. 11(1), pages 119-132, August.
    12. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    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. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
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    Cited by:

    1. Eisenhauer, Joseph G., 2006. "Risk aversion and prudence in the large," Research in Economics, Elsevier, vol. 60(4), pages 179-187, December.
    2. Christian Gollier & Miles S. Kimball, 2018. "New methods in the classical economics of uncertainty: comparing risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 5-23, May.
    3. Eisenhauer, Joseph G., 2010. "Rank-ordering of risk preferences with conventional and discrete measures," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(3), pages 291-297, August.

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    More about this item

    Keywords

    Risk Aversion; Stochastic dominance;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D30 - Microeconomics - - Distribution - - - General

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