Robust hidden Markov LQG problems

Lars Peter Hansen, Ricardo Mayer, Thomas Sargent
2010 Journal of Economic Dynamics and Control  
For linear quadratic Gaussian problems, this paper uses two risk-sensitivity operators defined by Hansen and Sargent (2007c) to construct decision rules that are robust to misspecifications of (1) transition dynamics for possibly hidden state variables, and (2) a probability density over hidden states induced by Bayes' law. Duality of risksensitivity to the multiplier min-max expected utility theory of Hansen and Sargent (2001) allows us to compute risk-sensitivity operators by solving
more » ... r zero-sum games. That the approximating model is a Gaussian joint probability density over sequences of signals and states gives important computational simplifications. We exploit a modified certainty equivalence principle to solve four games that differ in continuation value functions and discounting of time t increments to entropy. In Games I, II, and 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 describe how detection error probabilities can be used to calibrate the risk-sensitivity parameters that govern fear of model misspecification in hidden Markov models.
doi:10.1016/j.jedc.2010.05.004 fatcat:mpm3rfpx3jfqnf5j7dlps2amzy