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Asset pricing under smooth ambiguity in continuous time

Author

Listed:
  • Lars Peter Hansen

    (University of Chicago)

  • Jianjun Miao

    (Boston University)

Abstract

We study asset pricing implications of a revealing and tractable formulation of smooth ambiguity investor preferences in a continuous-time environment. Investors do not observe a hidden Markov state and instead make inferences about this state using past data. We show that ambiguity about this hidden state distribution alters investor decisions and equilibrium asset prices. Our continuous-time formulation allows us to apply recursive filtering and Hamilton–Jacobi–Bellman methods to solve the modified decision problem. Using such methods, we show how characterizations of portfolio allocations and local uncertainty-return tradeoffs change when investors are ambiguity-averse.

Suggested Citation

  • Lars Peter Hansen & Jianjun Miao, 2022. "Asset pricing under smooth ambiguity in continuous time," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 335-371, September.
    • Handle: RePEc:spr:joecth:v:74:y:2022:i:2:d:10.1007_s00199-022-01441-5
    DOI: 10.1007/s00199-022-01441-5
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    References listed on IDEAS

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    1. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    2. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    3. Hansen, Lars Peter & Sargent, Thomas J., 2011. "Robustness and ambiguity in continuous time," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1195-1223, May.
    4. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    5. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    6. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    7. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    8. repec:nas:journl:v:115:y:2018:p:9163-9168 is not listed on IDEAS
    9. Pierre Collin-Dufresne & Michael Johannes & Lars A. Lochstoer, 2016. "Parameter Learning in General Equilibrium: The Asset Pricing Implications," American Economic Review, American Economic Association, vol. 106(3), pages 664-698, March.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    12. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    13. Hengjie Ai, 2010. "Information Quality and Long‐Run Risk: Asset Pricing Implications," Journal of Finance, American Finance Association, vol. 65(4), pages 1333-1367, August.
    14. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
    15. Costis Skiadas, 2013. "Smooth Ambiguity Aversion toward Small Risks and Continuous-Time Recursive Utility," Journal of Political Economy, University of Chicago Press, vol. 121(4), pages 000.
    16. , & ,, 2011. "Intertemporal substitution and recursive smooth ambiguity preferences," Theoretical Economics, Econometric Society, vol. 6(3), September.
    17. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    18. 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..
    19. Michael Barnett & William Brock & Lars Peter Hansen & Harrison Hong, 2020. "Pricing Uncertainty Induced by Climate Change," The Review of Financial Studies, Society for Financial Studies, vol. 33(3), pages 1024-1066.
    20. Feldman, David, 1992. "Logarithmic Preferences, Myopic Decisions, and Incomplete Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(4), pages 619-629, December.
    21. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    22. Detemple, Jerome B, 1986. "Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
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    Cited by:

    1. Xepapadeas, Anastasios, 2024. "Uncertainty and climate change: The IPCC approach vs decision theory," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 109(C).
    2. Jin, Yurong & Yan, Jingzhou & Yan, Qianhui, 2024. "Unraveling ESG Ambiguity, Price Reaction, and Trading Volume," Finance Research Letters, Elsevier, vol. 61(C).
    3. Jianjun Miao, 2022. "Introduction to the special issue in honor of Larry Epstein," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 329-333, September.
    4. Luo, Deqing & Shan, Xun & Yan, Jingzhou & Yan, Qianhui, 2023. "Sustainable investment under ESG volatility and ambiguity," Economic Modelling, Elsevier, vol. 128(C).
    5. Arnon Archankul & Giorgio Ferrari & Tobias Hellmann & Jacco J. J. Thijssen, 2023. "Singular Control in a Cash Management Model with Ambiguity," Papers 2309.12014, arXiv.org.

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    More about this item

    Keywords

    Risk; Ambiguity; Robustness; Asset pricing; Portfolio allocation; Continuous time;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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