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Stochastic Dominance and Absolute Risk Aversion

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Abstract

In this paper we propose the in?mum 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 ?nd two utility functions in this class yielding opposite preference relations for the two distributions.

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Bibliographic Info

Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 602.03.

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Length: 27
Date of creation: 01 Oct 2003
Date of revision:
Handle: RePEc:aub:autbar:602.03

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Keywords: Risk aversion; Stochastic dominance;

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References

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  1. Caballé, Jordi & Pomansky, Alexey, 1995. "Mixed Risk Aversion," Working Paper Series 444, Research Institute of Industrial Economics.
  2. Meyer, Jack, 1975. "Increasing risk," Journal of Economic Theory, Elsevier, vol. 11(1), pages 119-132, August.
  3. 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 477-87, June.
  4. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  6. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  7. Lambert, Peter J. & Hey, John D., 1979. "Attitudes to risk," Economics Letters, Elsevier, vol. 2(3), pages 215-218.
  8. 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.
  9. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  11. Gollier, C. & Kimball, M.S., 1996. "New Methods in the Classical Economics of Uncertainty: Comparing Risks," Papers 96.412, Toulouse - GREMAQ.
  12. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  13. 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 Mathématique et Applications 97.53, Université Panthéon-Sorbonne (Paris 1).
  14. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January.
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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. 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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