IDEAS home Printed from https://ideas.repec.org/p/ags/uqsers/151163.html
   My bibliography  Save this paper

Increasing Uncertainty: A Definition

Author

Listed:
  • Grant, Simon
  • Quiggin, John

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.

Suggested Citation

  • Grant, Simon & Quiggin, John, 2004. "Increasing Uncertainty: A Definition," Risk and Sustainable Management Group Working Papers 151163, University of Queensland, School of Economics.
    • Handle: RePEc:ags:uqsers:151163
    DOI: 10.22004/ag.econ.151163
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/151163/files/WPR04_4.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.151163?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    3. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    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. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    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. 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.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    12. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    13. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    14. 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).
    15. 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.
    16. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
    17. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 47-65.
    18. 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.
    19. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    20. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    21. Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-127, March.
    22. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    23. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    24. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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 Economia Aplicada, Estudios de Economia Aplicada, vol. 29, pages 387(18á.)-3, Abril.
    2. Johanna Etner & Meglena Jeleva & Jean‐Marc Tallon, 2012. "Decision Theory Under Ambiguity," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 234-270, April.
    3. Bommier, Antoine & Chassagnon, Arnold & Le Grand, François, 2012. "Comparative risk aversion: A formal approach with applications to saving behavior," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1614-1641.
    4. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
    5. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    6. repec:awi:wpaper:0448 is not listed on IDEAS
    7. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    8. Zuber, Stéphane & Asheim, Geir B., 2012. "Justifying social discounting: The rank-discounted utilitarian approach," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1572-1601.
    9. Antoine Bommier & Francois Le Grand, "undated". "A Robust Approach to Risk Aversion," Working Papers ETH-RC-13-002, ETH Zurich, Chair of Systems Design.
    10. 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, May.
    11. Michèle Cohen & Isaac Meilijson, 2014. "Preference for safety under the Choquet model: in search of a characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 619-642, April.
    12. Jean Baccelli & Georg Schollmeyer & Christoph Jansen, 2022. "Risk aversion over finite domains," Theory and Decision, Springer, vol. 93(2), pages 371-397, September.
    13. Pavlo Blavatskyy, 2021. "A measure of ambiguity (Knightian uncertainty)," Theory and Decision, Springer, vol. 91(2), pages 153-171, September.
    14. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Papers 07-50, Sonderforschungsbreich 504.
    15. Marie-Charlotte Guetlein, 2016. "Comparative Risk Aversion in the Presence of Ambiguity," American Economic Journal: Microeconomics, American Economic Association, vol. 8(3), pages 51-63, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Grant, S. & Quiggin, J., 2001. "A Model-Free Definition of Increasing Uncertainty," Discussion Paper 2001-84, Tilburg University, Center for Economic Research.
    2. Moez Abouda & Elyess Farhoud, 2010. "Risk aversion and Relationships in model-free," Post-Print halshs-00492170, HAL.
    3. Moez Abouda & Elyess Farhoud, 2010. "Anti-comonotone random variables and anti-monotone risk aversion," Post-Print halshs-00497444, HAL.
    4. repec:awi:wpaper:0448 is not listed on IDEAS
    5. Xiangyu Qu, 2015. "A belief-based definition of ambiguity aversion," Theory and Decision, Springer, vol. 79(1), pages 15-30, July.
    6. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    7. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Sonderforschungsbereich 504 Publications 07-50, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
      • Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Papers 07-50, Sonderforschungsbreich 504.
    8. Jean Baccelli & Georg Schollmeyer & Christoph Jansen, 2022. "Risk aversion over finite domains," Theory and Decision, Springer, vol. 93(2), pages 371-397, September.
    9. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
    11. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    12. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    13. 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.
    14. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Trabelsi, Mohamed Ali, 2006. "Les nouveaux modèles de décision dans le risque et l’incertain : quel apport ? [The new models of decision under risk or uncertainty : What approach?]," MPRA Paper 25442, University Library of Munich, Germany.
    16. Michèle Cohen & Isaac Meilijson, 2014. "Preference for safety under the Choquet model: in search of a characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 619-642, April.
    17. Qu, Xiangyu, 2013. "Maxmin expected utility with additivity on unambiguous events," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 245-249.
    18. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    19. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Diversification preferences in the theory of choice," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 143-174, November.
    20. Trabelsi, Mohamed Ali, 2006. "Les nouveaux modèles de décision dans le risque et l’incertain : quel apport ? [The new models of decision under risk or uncertainty : What approach?]," MPRA Paper 25442, University Library of Munich, Germany.
    21. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.

    More about this item

    Keywords

    Environmental Economics and Policy; Risk and Uncertainty;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ags:uqsers:151163. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/decuqau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.