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Ordering Ambiguous Acts

Author

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  • Sujoy Mukerji

    (Queen Mary University of London)

  • Ian Jewitt

    (Nuffield College, Oxford University)

Abstract

We investigate what it means for one act to be more ambiguous than another. The question is evidently analogous to asking what makes one prospect riskier than another, but beliefs are neither objective nor representable by a unique probability. Our starting point is an abstract class of preferences constructed to be (strictly) partially ordered by a more ambiguity averse relation. First, we define two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse off but does not affect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely affects a more ambiguity averse DM more, as measured by the compensation they require to switch acts. Unlike more ambiguous (I), more ambiguous (II) does not require indifference of ambiguity neutral elements to the acts being compared. Second, we implement the abstract definitions to characterize more ambiguous (I) and (II) for two explicit preference families: a maxmin expected utility and smooth ambiguity. Thirdly, we give applications to the comparative statics of more ambiguous in a standard portfolio problem and a consumption-saving problem.

Suggested Citation

  • Sujoy Mukerji & Ian Jewitt, 2017. "Ordering Ambiguous Acts," Working Papers 828, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:828
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    Cited by:

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    2. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    3. Miao, Jianjun & Wang, Neng, 2011. "Risk, uncertainty, and option exercise," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 442-461, April.
    4. Hackbarth, Dirk & Miao, Jianjun, 2012. "The dynamics of mergers and acquisitions in oligopolistic industries," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 585-609.
    5. Loïc Berger & Louis Eeckhoudt, 2020. "Risk, Ambiguity, And The Value Of Diversification," Working Papers hal-02910906, HAL.
    6. Cherbonnier, Frédéric & Gollier, Christian, 2015. "Decreasing aversion under ambiguity," Journal of Economic Theory, Elsevier, vol. 157(C), pages 606-623.
    7. Kellner, Christian, 2015. "Tournaments as a response to ambiguity aversion in incentive contracts," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 627-655.
    8. Battigalli, P. & Francetich, A. & Lanzani, G. & Marinacci, M., 2019. "Learning and self-confirming long-run biases," Journal of Economic Theory, Elsevier, vol. 183(C), pages 740-785.
    9. Aflaki, Sam, 2013. "The effect of environmental uncertainty on the tragedy of the commons," Games and Economic Behavior, Elsevier, vol. 82(C), pages 240-253.
    10. Fujii, Tomoki, 2017. "Dynamic Poverty Decomposition Analysis: An Application to the Philippines," World Development, Elsevier, vol. 100(C), pages 69-84.
    11. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    12. Loic Berger, 2021. "What Is Partial Ambiguity?," Working Papers 2021-iRisk-01, IESEG School of Management.
    13. Loïc Berger, 2011. "Smooth Ambiguity Aversion in the Small and in the Large," Working Papers ECARES ECARES 2011-020, ULB -- Universite Libre de Bruxelles.
    14. L. A. Franzoni, 2016. "Optimal liability design under risk and ambiguity," Working Papers wp1048, Dipartimento Scienze Economiche, Universita' di Bologna.
    15. Loïc Berger & Louis Eeckhoudt, 2021. "Risk, Ambiguity, and the Value of Diversification," Management Science, INFORMS, vol. 67(3), pages 1639-1647, March.
    16. Simon Dietz & Falk Niehörster, 2021. "Pricing ambiguity in catastrophe risk insurance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 46(2), pages 112-132, September.
    17. Doriana Ruffino, 2014. "A Robust Capital Asset Pricing Model," Finance and Economics Discussion Series 2014-01, Board of Governors of the Federal Reserve System (U.S.).
    18. Sujoy Mukerji & Han Ozsoylev & Jean-Marc Tallon, 2018. "Trading ambiguity: a tale of two heterogeneities," Working Papers halshs-01935319, HAL.
    19. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    20. Alan Rogers & Matthew Ryan, 2012. "Additivity and Uncertainty," Economics Bulletin, AccessEcon, vol. 32(3), pages 1858-1864.
    21. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    22. Pavlo Blavatskyy, 2021. "A measure of ambiguity (Knightian uncertainty)," Theory and Decision, Springer, vol. 91(2), pages 153-171, September.
    23. Peter, Richard & Ying, Jie, 2020. "Do you trust your insurer? Ambiguity about contract nonperformance and optimal insurance demand," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 938-954.
    24. Takao Asano & Yusuke Osaki, 2020. "Portfolio allocation problems between risky and ambiguous assets," Annals of Operations Research, Springer, vol. 284(1), pages 63-79, January.

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    More about this item

    Keywords

    Ambiguity; Uncertainty; Knightian Uncertainty; Ambiguity Aversion; Uncertainty aversion; Ellsberg paradox; Comparative statics; Single-crossing; More ambiguous; Portfolio choice;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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