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Decreasing aversion under ambiguity

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  • Cherbonnier, Frédéric
  • Gollier, Christian

Abstract

Under which condition does the set of desirable uncertain prospects expand when wealth increases? We show that the decreasing concavity (DC) of the utility function u is necessary and sufficient in the α-maxmin expected utility model. In the smooth ambiguity aversion model with the ambiguity valuation function ϕ, the DC of u and of ϕ∘u is necessary and sufficient. An alternative classical definition of decreasing aversion is based on the hypothesis that the investment in a risky asset is increasing in wealth. We show that this hypothesis does not hold in general under ambiguity aversion, and that one needs to constrain the structure of ambiguity to obtain unambiguous results.

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  • Cherbonnier, Frédéric & Gollier, Christian, 2015. "Decreasing aversion under ambiguity," Journal of Economic Theory, Elsevier, vol. 157(C), pages 606-623.
    • Handle: RePEc:eee:jetheo:v:157:y:2015:i:c:p:606-623
    DOI: 10.1016/j.jet.2015.01.002
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    Cited by:

    1. Schmidt, Ulrich & Neyse, Levent & Aleknonyte, Milda, 2019. "Income inequality and risk taking: the impact of social comparison information," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 87(3), pages 283-297.
    2. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    3. Francesco Fabbri & Giulio Principi & Lorenzo Stanca, 2024. "Absolute and Relative Ambiguity Attitudes," Papers 2406.01343, arXiv.org, revised Jun 2024.
    4. Claudio A. Bonilla & Pablo A. Gutiérrez Cubillos, 2021. "The effects of ambiguity on entrepreneurship," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(1), pages 63-80, February.
    5. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2020. "Objective rationality foundations for (dynamic) alpha-MEU," Cowles Foundation Discussion Papers 2244R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2021.
    6. Wong, Kit Pong, 2016. "Ambiguity and the multinational firm," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 404-414.
    7. Baillon, Aurélien & Placido, Lætitia, 2019. "Testing constant absolute and relative ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 181(C), pages 309-332.
    8. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2022. "Objective rationality foundations for (dynamic) α-MEU," Journal of Economic Theory, Elsevier, vol. 200(C).
    9. Paweł Dziewulski & John K.‐H. Quah, 2024. "Comparative Statics With Linear Objectives: Normality, Complementarity, and Ranking Multi‐Prior Beliefs," Econometrica, Econometric Society, vol. 92(1), pages 167-200, January.
    10. Manel Baucells & Rakesh K. Sarin, 2019. "The Myopic Property in Decision Models," Decision Analysis, INFORMS, vol. 16(2), pages 128-141, June.
    11. Christian Gollier & Miles S. Kimball, 2018. "New methods in the classical economics of uncertainty: comparing risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 5-23, May.
    12. Christoph Große Steffen & Maximilian Podstawski, 2016. "Ambiguity and Time-Varying Risk Aversion in Sovereign Debt Markets," Discussion Papers of DIW Berlin 1602, DIW Berlin, German Institute for Economic Research.
    13. Ghosh, Gagan & Liu, Heng, 2021. "Sequential auctions with ambiguity," Journal of Economic Theory, Elsevier, vol. 197(C).
    14. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2016. "Absolute and Relative Ambiguity Aversion: A Preferential Approach," Working Papers 578, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    15. Rachel J. Huang & Arthur Snow & Larry Y. Tzeng, 2017. "Advantageous Selection in Insurance Markets with Compound Risk," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 42(2), pages 171-192, September.
    16. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2019. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2180, Cowles Foundation for Research in Economics, Yale University.
    17. Chiaki Hara & Toshiki Honda, 2022. "Implied Ambiguity: Mean-Variance Inefficiency and Pricing Errors," Management Science, INFORMS, vol. 68(6), pages 4246-4260, June.
    18. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo, 2022. "Ambiguity aversion and wealth effects," Journal of Economic Theory, Elsevier, vol. 199(C).
    19. Pawel Dziewulski & John K. H. Quah, 2019. "Supermodular correspondences and comparison of multi-prior beliefs," Working Paper Series 0619, Department of Economics, University of Sussex Business School.

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    More about this item

    Keywords

    Decreasing concavity; Portfolio choice; α-MEU; Smooth ambiguity aversion; Maxmin;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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