Journal of Risk and Uncertainty

, Volume 38, Issue 1, pp 27–37 | Cite as

Risk aversion in the small and in the large: Calibration results for betweenness functionals

Article

Abstract

A reasonable level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. This was demonstrated by Rabin (Econometrica 68:1281–1292, 2000) for expected utility theory. Later, Safra and Segal (Econometrica, 2008) extended this result by showing that similar arguments apply to many non-expected utility theories, provided they are Gâteaux differentiable. In this paper we drop the differentiability assumption and by restricting attention to betweenness theories we show that much weaker conditions are sufficient for the derivation of similar calibration results.

Keywords

Risk aversion Calibration results Betweenness functionals 

References

  1. Chew, S. H. (1983). A generalization of the quasilinear mean with applications to the measurement of income inequality and decision theory resolving the Allais paradox. Econometrica, 51, 1065–1092.CrossRefGoogle Scholar
  2. Chew, S. H. (1989). Axiomatic utility theories with the betweenness property. Annals of Operations Research, 19, 273–298.CrossRefGoogle Scholar
  3. Chew, S. H., Epstein, L. G., & Segal, U. (1991). Mixture symmetry and quadratic utility. Econometrica, 59, 139–163.CrossRefGoogle Scholar
  4. Cox, J. C., & Sadiraj, V. (2006). Small-and large-stakes risk aversion: Implications of concavity calibration for decision theory. Games and Economic Behavior, 56, 45–60.CrossRefGoogle Scholar
  5. Dekel, E. (1986). An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom. Journal of Economic Theory, 40, 304–318.CrossRefGoogle Scholar
  6. Epstein, L. G. (1992). Behavior under risk: Recent developments in theory and applications. In J. J. Laffont (Ed.), Advances in economic theory (Vol. II, pp. 1–63). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  7. Fishburn, P. C. (1983). Transitive measurable utility. Journal of Economic Theory, 31, 293–317.CrossRefGoogle Scholar
  8. Foster, D. P., & Hart, S. (2007). An operational measure of riskiness. The Hebrew University of JerusalemGoogle Scholar
  9. Guiso, L., Jappelli, T., & Terlizzese, D. (1996). Income risk, borrowing constraints, and portfolio choice. American Economic Review, 86, 158–172.Google Scholar
  10. Gul, F. (1991). A theory of disappointment aversion. Econometrica, 59, 667–686.CrossRefGoogle Scholar
  11. Hochguertel, S. (2003). Precautionary motives and protfolio decisions. Journal of Applied Econometrics, 18, 61–77.CrossRefGoogle Scholar
  12. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263–291.CrossRefGoogle Scholar
  13. Machina, M. J. (1982). ‘Expected utility’ analysis without the independence axiom. Econometrica, 50, 277–323.CrossRefGoogle Scholar
  14. Paiella, M., & Guiso, L. (2001). Risk aversion, wealth and background risk. Mimeo.Google Scholar
  15. Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior and Organization, 3, 323–343.CrossRefGoogle Scholar
  16. Rabin, M. (2000). Risk aversion and expected utility theory: A calibration result. Econometrica, 68, 1281–1292.CrossRefGoogle Scholar
  17. Rabin, M., & Thaler, R. H. (2001). Risk aversion. Journal of Economic Perspectives, 15, 219–232.CrossRefGoogle Scholar
  18. Rubinstein, A. (2006). Dilemmas of an economic theorist. Econometrica, 74, 865–883.CrossRefGoogle Scholar
  19. Safra, Z., & Segal, U. (1998). Constant risk aversion. Journal of Economic Theory, 83, 19–42.CrossRefGoogle Scholar
  20. Safra, Z., & Segal, U. (2008). Calibration results for non expected utility preferences. Econometrica, 76, 1143–1166.Google Scholar
  21. Smorodinsky, R. (2000). The reflection effect for constant risk averse agents. Mathematical Social Sciences, 40, 265–276.CrossRefGoogle Scholar
  22. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.The College of Management and Tel Aviv UniversityTel AvivIsrael
  2. 2.Department of EconomicsBoston CollegeChestnut HillUSA

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