IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v56y2014i2p275-289.html
   My bibliography  Save this article

The dual theory of the smooth ambiguity model

Author

Listed:
  • Hideki Iwaki
  • Yusuke Osaki

Abstract

This paper studies the “dual” theory of the smooth ambiguity model introduced by Klibanoff et al. (Econometrica 73:1849–1892, 2005 ). Unlike the original model, we characterize attitudes toward ambiguity captured by second-order probabilities. First, we give a set of axioms to derive a dual representation of the smooth ambiguity model. Second, we present a characterization of ambiguity aversion. Last, as an application of our dual model to a portfolio problem, we conduct comparative static predictions which give sufficient conditions to guarantee that an increase in smooth ambiguity aversion decreases the optimal portfolio. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Hideki Iwaki & Yusuke Osaki, 2014. "The dual theory of the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 275-289, June.
    • Handle: RePEc:spr:joecth:v:56:y:2014:i:2:p:275-289
    DOI: 10.1007/s00199-013-0779-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-013-0779-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-013-0779-6?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2011. "Definitions of ambiguous events and the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 399-424, October.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 73-85.
    4. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, vol. 22(10), pages 1064-1073, June.
    5. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    6. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    7. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, January.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    11. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    12. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1329-1344.
    13. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    14. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    15. Leandro Nascimento & Gil Riella, 2013. "Second-order ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1005-1037, April.
    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. Guan, Guohui & Li, Bin, 2022. "Equilibrium investment and reinsurance strategies under smooth ambiguity with a general second-order distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    2. Louis Eeckhoudt & Liqun Liu & Jack Meyer, 2017. "Restricted increases in risk aversion and their application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 161-181, June.
    3. Dennis W. Jansen & Liqun Liu, 2022. "Portfolio choice in the model of expected utility with a safety-first component," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 187-207, June.
    4. Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
    5. Iwaki, Hideki & Osaki, Yusuke, 2017. "Comparative statics and portfolio choices under the phantom decision model," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 1-8.
    6. Suzuki, Masataka, 2018. "Continuous-time smooth ambiguity preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 30-44.
    7. Kit Pong Wong, 2015. "A Smooth Ambiguity Model Of The Competitive Firm," Bulletin of Economic Research, Wiley Blackwell, vol. 67(S1), pages 97-110, December.
    8. Huang, Yi-Chieh & Tzeng, Larry Y. & Zhao, Lin, 2015. "Comparative ambiguity aversion and downside ambiguity aversion," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 257-269.
    9. Nicole Bauerle & Antje Mahayni, 2023. "Optimal investment in ambiguous financial markets with learning," Papers 2303.08521, arXiv.org, revised Feb 2024.
    10. 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.

    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. Yehuda Izhakian & Zur Izhakian, 2015. "Decision making in phantom spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 59-98, January.
    2. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    3. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    4. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    5. Asano, Takao & Osaki, Yusuke, 2021. "Optimal investment under ambiguous technology shocks," European Journal of Operational Research, Elsevier, vol. 293(1), pages 304-311.
    6. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    7. Massimo Marinacci, 2015. "Model Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1022-1100, December.
    8. 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.
    9. Victor Filipe Martins da Rocha & Rafael Mouallem, 2020. "Second-Order Beliefs and Second-Order Expected Utility," Working Papers hal-02922263, HAL.
    10. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    11. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1329-1344.
    12. Takao Asano & Yusuke Osaki, 2017. "Portfolio Allocation Problems between Risky Ambiguous Assets," KIER Working Papers 975, Kyoto University, Institute of Economic Research.
    13. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    14. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    15. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    16. Dillenberger, David & Segal, Uzi, 2017. "Skewed noise," Journal of Economic Theory, Elsevier, vol. 169(C), pages 344-364.
    17. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    18. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    19. Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
    20. Huang, Yi-Chieh & Tzeng, Larry Y. & Zhao, Lin, 2015. "Comparative ambiguity aversion and downside ambiguity aversion," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 257-269.

    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:spr:joecth:v:56:y:2014:i:2:p:275-289. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.