## 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 language | English (US) |
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Pages (from-to) | 1951-1966 |

Number of pages | 16 |

Journal | Journal of Economic Dynamics and Control |

Volume | 34 |

Issue number | 10 |

DOIs | |

State | Published - 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