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Increasing Uncertainty: A Definition

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  • Simon Grant

    ()
    (Department of Economics, Rice University)

  • John Quiggin

    ()
    (Department of Economics, University of Queensland)

Abstract

We present a definition of increasing uncertainty, in which an elementary increase in the uncertainty of any act corresponds to the addition of an `elementary bet' that increases consumption by a fixed amount in (relatively) `good' states and decreases consumption by a fixed (and possibly different) amount in (relatively) `bad' states. This definition naturally gives rise to a dual definition of comparative aversion to uncertainty. We characterize this definition for a popular class of generalized models of choice under uncertainty.

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Bibliographic Info

Paper provided by Risk and Sustainable Management Group, University of Queensland in its series Risk & Uncertainty Working Papers with number WPR04_4.

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Date of creation: May 2004
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Handle: RePEc:rsm:riskun:r04_4

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Keywords: uncertainty; ambiguity; risk; non-expected utility;

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References

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  1. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
  2. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  3. 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.
  4. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  5. 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).
  6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  7. repec:hal:cesptp:halshs-00212281 is not listed on IDEAS
  8. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
  9. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  11. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  12. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
  13. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  14. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  15. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  16. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
  17. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer, vol. 20(1), pages 47-65.
  18. 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.
  19. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
  20. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good risks: An interpretation of multivariate risk and risk aversion without the Independence axiom," Journal of Economic Theory, Elsevier, vol. 56(2), pages 338-351, April.
  21. 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.
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Citations

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Cited by:
  1. Antoine Bommier & François Le Grand, 2013. "A Robust Approach to Risk Aversion," CER-ETH Economics working paper series 13/172, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  2. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Sonderforschungsbereich 504 Publications 07-50, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
    • Jürgen Eichberger & David Kelsey, 2007. "Ambiguity," Working Papers 0448, University of Heidelberg, Department of Economics, revised Jul 2007.
  3. Antoine Bommier & Arnold Chassagnon & François Le Grand, 2010. "Comparative Risk Aversion: A Formal Approach with Applications to Saving Behaviors," CER-ETH Economics working paper series 10/134, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  4. repec:hal:journl:halshs-00429573 is not listed on IDEAS
  5. Michèle Cohen & Isaac Meilijson, 2014. "Preference for safety under the Choquet model: in search of a characterization," Economic Theory, Springer, vol. 55(3), pages 619-642, April.
  6. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
  7. Stéphane Zuber & Geir B. Asheim, 2010. "Justifying Social Discounting: The Rank-Discounted Utilitarian Approach," CESifo Working Paper Series 3192, CESifo Group Munich.
  8. Gil-Lacruz, Ana I. & Gil-Lacruz, Marta, 2011. "Internal Inconsistency and Risk Aversion: Implications on Smoking Decisions/Consistencia interna y aversión al riesgo: implicaciones en la decisión de fumar," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 387 (18 pá, Abril.
  9. Bommier, Antoine & Zuber, Stéphane, 2009. "The Pareto Principle of Optimal Inequality," TSE Working Papers 09-132, Toulouse School of Economics (TSE).

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