Robust control and model misspecification

Lars Peter Hansen, Thomas Sargent, Gauhar Turmuhambetova, Noah Williams

    Research output: Contribution to journalArticle

    Abstract

    A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler [Maxmin expected utility with non-unique prior, J. Math. Econ. 18 (1989) 141-153], and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40 (5) (1995) 968-971]. To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and nonsequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.

    Original languageEnglish (US)
    Pages (from-to)45-90
    Number of pages46
    JournalJournal of Economic Theory
    Volume128
    Issue number1
    DOIs
    StatePublished - May 2006

    Fingerprint

    Model misspecification
    Robust control
    Decision rules
    Perturbation
    Maxmin expected utility
    Zero-sum game
    Martingale
    Discrete-time
    Decision maker
    Relative entropy
    Risk sensitivity
    Expected utility theory
    Control theory

    Keywords

    • Commitment
    • Entropy
    • Martingale
    • Model uncertainty
    • Risk-sensitivity
    • Robustness
    • Time inconsistency

    ASJC Scopus subject areas

    • Economics and Econometrics

    Cite this

    Hansen, L. P., Sargent, T., Turmuhambetova, G., & Williams, N. (2006). Robust control and model misspecification. Journal of Economic Theory, 128(1), 45-90. https://doi.org/10.1007/s11149-006-0008-3

    Robust control and model misspecification. / Hansen, Lars Peter; Sargent, Thomas; Turmuhambetova, Gauhar; Williams, Noah.

    In: Journal of Economic Theory, Vol. 128, No. 1, 05.2006, p. 45-90.

    Research output: Contribution to journalArticle

    Hansen, LP, Sargent, T, Turmuhambetova, G & Williams, N 2006, 'Robust control and model misspecification', Journal of Economic Theory, vol. 128, no. 1, pp. 45-90. https://doi.org/10.1007/s11149-006-0008-3
    Hansen LP, Sargent T, Turmuhambetova G, Williams N. Robust control and model misspecification. Journal of Economic Theory. 2006 May;128(1):45-90. https://doi.org/10.1007/s11149-006-0008-3
    Hansen, Lars Peter ; Sargent, Thomas ; Turmuhambetova, Gauhar ; Williams, Noah. / Robust control and model misspecification. In: Journal of Economic Theory. 2006 ; Vol. 128, No. 1. pp. 45-90.
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