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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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  1. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  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. Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997. "New Tools to Better Model Behavior Under Risk and UNcertainty: An Oevrview," Papiers d'Economie Mathématique et Applications 97.55, Université Panthéon-Sorbonne (Paris 1).
  4. Klaus Nehring & Michael Magill & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 978, University of California, Davis, Department of Economics.
  5. Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research.
  6. 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.
  7. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  8. 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.
  9. 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).
  10. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
  11. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  12. 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.
  13. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  14. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
  15. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer, vol. 20(1), pages 47-65.
  16. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  17. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  18. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  19. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  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. 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.
  22. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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Cited by:
  1. Antoine Bommier & Stéphane Zuber, 2012. "The Pareto Principle Of Optimal Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(2), pages 593-608, 05.
  2. Bommier, Antoine & Chassagnon, Arnold & Le Grand, François, 2010. "Comparative Risk Aversion: A Formal Approach with Applications to Savings Behaviors," TSE Working Papers 10-141, Toulouse School of Economics (TSE).
  3. 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.
  4. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
  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. 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.
  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. repec:hal:journl:halshs-00429573 is not listed on IDEAS

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