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Optimal Learning under Robustness and Time-Consistency

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  • Larry G. Epstein
  • Shaolin Ji

Abstract

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed-form, with a focus on two specific settings: Ellsberg's two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.

Suggested Citation

  • Larry G. Epstein & Shaolin Ji, 2017. "Optimal Learning under Robustness and Time-Consistency," Papers 1708.01890, arXiv.org, revised Mar 2019.
  • Handle: RePEc:arx:papers:1708.01890
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    References listed on IDEAS

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    1. Drew Fudenberg & Philipp Strack & Tomasz Strzalecki, 2018. "Speed, Accuracy, and the Optimal Timing of Choices," American Economic Review, American Economic Association, vol. 108(12), pages 3651-3684, December.
    2. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    3. Trautmann, Stefan T. & Zeckhauser, Richard J., 2013. "Shunning uncertainty: The neglect of learning opportunities," Games and Economic Behavior, Elsevier, vol. 79(C), pages 44-55.
    4. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
    5. Butler, Jeff & Guiso, Luigi & Jappelli, Tullio, 2013. "Manipulating Reliance on Intuition Reduces Risk and Ambiguity Aversion," CEPR Discussion Papers 9461, C.E.P.R. Discussion Papers.
    6. Jeffrey Butler & Luigi Guiso & Tullio Jappelli, 2014. "The role of intuition and reasoning in driving aversion to risk and ambiguity," Theory and Decision, Springer, vol. 77(4), pages 455-484, December.
    7. 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.
    8. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    9. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    10. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    11. Mark Schneider & Jonathan W. Leland & Nathaniel T. Wilcox, 2018. "Ambiguity framed," Journal of Risk and Uncertainty, Springer, vol. 57(2), pages 133-151, October.
      • Mark Schneider & Jonathan Leland & Nathaniel T. Wilcox, 2016. "Ambiguity Framed," Working Papers 16-11, Chapman University, Economic Science Institute.
    12. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
    13. Milica Milosavljevic & Jonathan Malmaud & Alexander Huth & Christof Koch & Antonio Rangel, 2010. "The Drift Diffusion Model can account for the accuracy and reaction time of value-based choices under high and low time pressure," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 5(6), pages 437-449, October.
    14. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 97-115, April.
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    16. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
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    18. Ariel Rubinstein, 2016. "A Typology of Players: Between Instinctive and Contemplative," The Quarterly Journal of Economics, Oxford University Press, vol. 131(2), pages 859-890.
    19. 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.
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    21. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "Erratum to: The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 117-117, April.
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    Cited by:

    1. Luis H. R. Alvarez E. & Soren Christensen, 2019. "The Impact of Ambiguity on the Optimal Exercise Timing of Integral Option Contracts," Papers 1906.07533, arXiv.org.
    2. Luis H. R. Alvarez E. & Soren Christensen, 2019. "A Class of Solvable Multidimensional Stopping Problems in the Presence of Knightian Uncertainty," Papers 1907.04046, arXiv.org.
    3. Roxane Bricet, 2018. "The price for instrumentally valuable information," THEMA Working Papers 2018-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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