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New Formulations of Ambiguous Volatility with an Application to Optimal Dynamic Contracting

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  • Peter G. Hansen

Abstract

I introduce novel preference formulations which capture aversion to ambiguity about unknown and potentially time-varying volatility. I compare these preferences with Gilboa and Schmeidler's maxmin expected utility as well as variational formulations of ambiguity aversion. The impact of ambiguity aversion is illustrated in a simple static model of portfolio choice, as well as a dynamic model of optimal contracting under repeated moral hazard. Implications for investor beliefs, optimal design of corporate securities, and asset pricing are explored.

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  • Peter G. Hansen, 2021. "New Formulations of Ambiguous Volatility with an Application to Optimal Dynamic Contracting," Papers 2101.12306, arXiv.org.
  • Handle: RePEc:arx:papers:2101.12306
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    References listed on IDEAS

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    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. Peter M. Demarzo & Michael J. Fishman & Zhiguo He & Neng Wang, 2012. "Dynamic Agency and the q Theory of Investment," Journal of Finance, American Finance Association, vol. 67(6), pages 2295-2340, December.
    5. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 345-390.
    6. Lars Peter Hansen & Thomas J Sargent, 2014. "Three Types of Ambiguity," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 11, pages 379-430, World Scientific Publishing Co. Pte. Ltd..
    7. Michael Woodford, 2010. "Robustly Optimal Monetary Policy with Near-Rational Expectations," American Economic Review, American Economic Association, vol. 100(1), pages 274-303, March.
    8. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    9. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    10. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    11. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    12. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    13. Xiaohong Chen & Lars Peter Hansen & Peter G. Hansen, 2020. "Robust identification of investor beliefs," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 117(52), pages 33130-33140, December.
    14. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    15. Hansen, Lars Peter & Sargent, Thomas J. & Wang, Neng E., 2002. "Robust Permanent Income And Pricing With Filtering," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 40-84, February.
    16. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    17. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
    18. Daniel, Kent & Titman, Sheridan, 1997. "Evidence on the Characteristics of Cross Sectional Variation in Stock Returns," Journal of Finance, American Finance Association, vol. 52(1), pages 1-33, March.
    19. Marcel Nutz, 2010. "Random G-expectations," Papers 1009.2168, arXiv.org, revised Sep 2013.
    20. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    21. Berger, Allen N & Udell, Gregory F, 1995. "Relationship Lending and Lines of Credit in Small Firm Finance," The Journal of Business, University of Chicago Press, vol. 68(3), pages 351-381, July.
    22. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    23. Augustin Landier & David Thesmar, 2009. "Financial Contracting with Optimistic Entrepreneurs," The Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 117-150, January.
    24. Peter M. DeMarzo & Michael J. Fishman, 2007. "Optimal Long-Term Financial Contracting," The Review of Financial Studies, Society for Financial Studies, vol. 20(6), pages 2079-2128, November.
    25. Martin Szydlowski, 2012. "Ambiguity in Dynamic Contracts," Discussion Papers 1543, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    26. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    27. Tobias Adrian & Mark M. Westerfield, 2009. "Disagreement and Learning in a Dynamic Contracting Model," The Review of Financial Studies, Society for Financial Studies, vol. 22(10), pages 3873-3906, October.
    28. John Y. Zhu, 2013. "Optimal Contracts with Shirking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 812-839.
    29. Nils Friewald & Christian Wagner & Josef Zechner, 2014. "The Cross-Section of Credit Risk Premia and Equity Returns," Journal of Finance, American Finance Association, vol. 69(6), pages 2419-2469, December.
    30. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    31. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
    32. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    33. Wolitzky, Alexander, 2016. "Mechanism design with maxmin agents: theory and an application to bilateral trade," Theoretical Economics, Econometric Society, vol. 11(3), September.
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