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Optimal Learning Under Robustness and Time-Consistency

Author

Listed:
  • Larry G. Epstein

    (Department of Economics, Boston University, Boston, Massachusetts 02215)

  • Shaolin Ji

    (Zhongtai Securities Institute of Financial Studies, Shandong University, 250100 Jinan, China)

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, 2022. "Optimal Learning Under Robustness and Time-Consistency," Operations Research, INFORMS, vol. 70(3), pages 1317-1329, May.
  • Handle: RePEc:inm:oropre:v:70:y:2022:i:3:p:1317-1329
    DOI: 10.1287/opre.2019.1899
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    Cited by:

    1. 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.
    2. 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.
    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.
    4. Farzad Pourbabaee, 2021. "Robust Experimentation in the Continuous Time Bandit Problem," Papers 2104.00102, arXiv.org.
    5. 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.

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