Model uncertainty, also known as Knightian uncertainty, has become a major research topic in recent years. On the decision-theoretic side, various approaches show how one can successfully capture model uncertainty with the help of mathematical models. The lecture reviews recent model of preferences under Knightian uncertainty. These approaches are closely related to attempts to quantify risk in finance.
A particular focus will be on the so-called smooth model, an ambiguity-averse version of a secondorder Bayesian Ansatz, that goes back to Klibanoff, Marinacci, and Mukerji (Econometrica 2005). We will study its axiomatic foundations and discuss the relationship of this approach with statistics, in particular the issue of identification of models (Denti, Pomatto, Econometrica 2022). Moreover, we show how the smooth model is related to variational and coherent risk measures.
We then investigate consequences of model uncertainty for the insurance market. We study the case where the typical consumer in the economy is ambiguity-averse with smooth ambiguity preferences and the set of priors is point identified, i.e., the true law can be recovered ex post empirically from observed events. The identifiability of models allows to write insurance contracts on models, with important economic consequences. We are able to construct a representative agent who, in general, has also smooth ambiguity preferences, yet with a model-dependent ambiguity attitude. We illustrate our results in the classic Wilson framework of risk sharing where the representative agent has modelindependent ambiguity attitude and insurance against ambiguity can be explicitly computed.
