Quantifying the Impact of Model Misspecification

Probabilistic models describing the future evolution of financial markets are not given by nature, but need to be chosen by market participants. This choice is complex and usually subject to some error, for instance, as not enough data are available for an accurate estimation. The resulting lack of confidence in the selection of the model goes under the name model uncertainty and is the topic of this project. We plan to develop a theory that aims at minimizing the impact of model uncertainty for problems typically considered in mathematical finance such as utility maximization or computing the fair price / monetary risk of financial positions. This is done in two parts. In the first part, we analyze how sensitive such problems are with respect to different types of errors that arise in model selection. In particular, this will improve our understanding which types of errors are more serious and should therefore be avoided. In the second and main part, we plan to develop statistical procedures, specifically tailored to given problems in mathematical finance, that avoid serious errors in the model selection.