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Robustness and ambiguity in continuous time

Author

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  • Hansen, Lars Peter
  • Sargent, Thomas J.
Abstract
We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24] and [25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:3:p:1195-1223
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    References listed on IDEAS

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    1. Lars Peter Hansen & Thomas J Sargent, 2014. "Beliefs, Doubts and Learning: Valuing Macroeconomic Risk," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 10, pages 331-377, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. 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.
    4. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean‐Marc Tallon, 2018. "Ambiguity and the historical equity premium," Quantitative Economics, Econometric Society, vol. 9(2), pages 945-993, July.
    5. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    6. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    7. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    8. Timothy Cogley & Riccardo Colacito & Lars Peter Hansen & Thomas J. Sargent, 2008. "Robustness and U.S. Monetary Policy Experimentation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(8), pages 1599-1623, December.
    9. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    10. 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..
    11. Hansen, Lars Peter & Sargent, Thomas J., 2005. "Robust estimation and control under commitment," Journal of Economic Theory, Elsevier, vol. 124(2), pages 258-301, October.
    12. Lars Peter Hansen & Thomas J Sargent, 2014. "Doubts or Variability?," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 7, pages 217-256, World Scientific Publishing Co. Pte. Ltd..
    13. Li-Lin Ku & Chien-Pai Han, 2008. "Robust testing procedures of process locations," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(5), pages 579-595, October.
    14. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 391-401.
    15. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    16. 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..
    17. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, April.
    18. Lars Peter Hansen & Thomas J Sargent, 2014. "Fragile Beliefs and the Price of Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 9, pages 293-330, World Scientific Publishing Co. Pte. Ltd..
    19. Hans, Erwin & Wullink, Gerhard & van Houdenhoven, Mark & Kazemier, Geert, 2008. "Robust surgery loading," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1038-1050, March.
    20. Lars Peter Hansen, 2007. "Beliefs, Doubts and Learning: Valuing Economic Risk," NBER Working Papers 12948, National Bureau of Economic Research, Inc.
    21. Thomas J. Sargent & Riccardo Colacito & Lars P. Hansen & Timothy Cogley, 2008. "Robustness and US Monetary," 2008 Meeting Papers 228, Society for Economic Dynamics.
    22. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    23. Lars Peter Hansen & Thomas J. Sargent, 2008. "Time Inconsistency of Robust Control?," Chapters, in: Roger E.A. Farmer (ed.), Macroeconomics in the Small and the Large, chapter 7, Edward Elgar Publishing.
    24. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    25. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    26. Truman F. Bewley, 1988. "Knightian Decision Theory and Econometric Inference," Cowles Foundation Discussion Papers 868, Cowles Foundation for Research in Economics, Yale University.
    27. 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.
    28. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    29. Truman F. Bewley, 1987. "Knightian Decision Theory, Part II. Intertemporal Problems," Cowles Foundation Discussion Papers 835, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    2. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    3. Michael Barnett & Greg Buchak & Constantine Yannelis, 2023. "Epidemic responses under uncertainty," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 120(2), pages 2208111120-, January.
    4. Farzad Pourbabaee, 2022. "Robust experimentation in the continuous time bandit problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 151-181, February.
    5. Laurence Carassus & Johannes Wiesel, 2023. "Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity," Papers 2306.01503, arXiv.org, revised Jan 2024.
    6. Li, Jing, 2018. "Essays on model uncertainty in financial models," Other publications TiSEM 202cd910-7ef1-4db4-94ae-d, Tilburg University, School of Economics and Management.
    7. Yacine Aït-Sahalia & Felix Matthys & Emilio Osambela & Ronnie Sircar, 2021. "When Uncertainty and Volatility Are Disconnected: Implications for Asset Pricing and Portfolio Performance," Finance and Economics Discussion Series 2021-063, Board of Governors of the Federal Reserve System (U.S.).
    8. Oleg Itskhoki & Dmitry Mukhin, 2021. "Exchange Rate Disconnect in General Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2183-2232.
    9. Marco Paolo Tucci, 2019. "The usual robust control framework in discrete time: Some interesting results," Department of Economics University of Siena 815, Department of Economics, University of Siena.
    10. Junichi Imai, 2022. "A Numerical Method for Hedging Bermudan Options under Model Uncertainty," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 893-916, June.
    11. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    12. Thomas Kruse & Judith C. Schneider & Nikolaus Schweizer, 2015. "What's in a ball? Constructing and characterizing uncertainty sets," Papers 1510.01675, arXiv.org.
    13. Jang, Bong-Gyu & Lee, Seungkyu & Lim, Byung Hwa, 2016. "Robust consumption and portfolio rules with time-varying model confidence," Finance Research Letters, Elsevier, vol. 18(C), pages 342-352.
    14. 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.
    15. Manel Baucells & Rakesh K. Sarin, 2019. "The Myopic Property in Decision Models," Decision Analysis, INFORMS, vol. 16(2), pages 128-141, June.
    16. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
    17. 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.
    18. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
    19. Farzad Pourbabaee, 2021. "Robust Experimentation in the Continuous Time Bandit Problem," Papers 2104.00102, arXiv.org.
    20. Georgios I. Papayiannis, 2022. "Static Hedging of Freight Risk under Model Uncertainty," Papers 2207.00862, arXiv.org.
    21. Yanwei Jia, 2024. "Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty," Papers 2404.12598, arXiv.org.
    22. 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.
    23. Flor, Christian Riis & Hesel, Søren, 2015. "Uncertain dynamics, correlation effects, and robust investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 278-298.

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