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Calibration Results for Betweenness Functionals

Author

Listed:
  • Zvi Safra

    (Tel Aviv University)

  • Uzi Segal

    () (Boston College)

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 for expected utility theory. Later, Safra and Segal extended this result by showing that similar arguments apply to almost all non-expected utility theories, provided they are Gateaux 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.

Suggested Citation

  • Zvi Safra & Uzi Segal, 2008. "Calibration Results for Betweenness Functionals," Boston College Working Papers in Economics 683, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:683
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    References listed on IDEAS

    as
    1. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    2. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    3. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    4. Zvi Safra & Uzi Segal, 2008. "Calibration Results for Non-Expected Utility Theories," Econometrica, Econometric Society, vol. 76(5), pages 1143-1166, September.
    5. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    6. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    7. Luigi Guiso & Monica Paiella, 2008. "Risk Aversion, Wealth, and Background Risk," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1109-1150, December.
    8. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    9. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
    12. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
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    Keywords

    risk aversion; betweenness;

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