Robust estimation and control under commitment

Lars Peter Hansen, Thomas J. Sargent

    Research output: Contribution to journalArticle

    Abstract

    In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Başar and P. Bernhard [H-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].

    Original languageEnglish (US)
    Pages (from-to)258-301
    Number of pages44
    JournalJournal of Economic Theory
    Volume124
    Issue number2
    DOIs
    StatePublished - Oct 2005

    Keywords

    • Bayes' law
    • Commitment
    • Entropy
    • Learning
    • Model uncertainty
    • Risk-sensitivity
    • Robustness
    • Time inconsistency

    ASJC Scopus subject areas

    • Economics and Econometrics

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