Robust hidden Markov LQG problems

Lars Peter Hansen, Ricardo Mayer, Thomas Sargent

    Research output: Contribution to journalArticle

    Abstract

    For linear quadratic Gaussian problems, this paper uses two risk-sensitivity operators defined by Hansen and Sargent (2007b) to construct decision rules that are robust to misspecifications of (1) transition dynamics for state variables and (2) a probability density over hidden states induced by Bayes' law. Duality of risk sensitivity to the multiplier version of min-max expected utility theory of Hansen and Sargent (2001) allows us to compute risk-sensitivity operators by solving two-player zero-sum games. Because the approximating model is a Gaussian probability density over sequences of signals and states, we can exploit a modified certainty equivalence principle to solve four games that differ in continuation value functions and discounting of time t increments to entropy. The different games express different dimensions of concerns about robustness. All four games give rise to time consistent worst-case distributions for observed signals. But in Games I-III, the minimizing players' worst-case densities over hidden states are time inconsistent, while Game IV is an LQG version of a game of Hansen and Sargent (2005) that builds in time consistency. We show how detection error probabilities can be used to calibrate the risk-sensitivity parameters that govern fear of model misspecification in hidden Markov models.

    Original languageEnglish (US)
    Pages (from-to)1951-1966
    Number of pages16
    JournalJournal of Economic Dynamics and Control
    Volume34
    Issue number10
    DOIs
    StatePublished - Oct 2010

    Keywords

    • Certainty equivalence
    • Entropy
    • Hidden Markov models
    • Kalman filter
    • Misspecification
    • Robustness

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Control and Optimization
    • Applied Mathematics

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