Making Decisions Under Model Misspecification

We use decision theory to confront uncertainty that is sufficiently broad to incorporate "models as approximations." We presume the existence of a featured collection of what we call "structured models" that have explicit substantive motivations. The decision-maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. We then extend our analysis beyond the max-min case allowing for a more general criterion that encompasses a Bayesian formulation.