Robust Control and Model Misspecification

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 and are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler (1989), and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent (1995). To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and non-sequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.