Abstracts

In this work we extend the convex analysis approach to robust utility maximization of final wealth in a financial market model, to the case where the set of uncertain measures (model uncertainty) does not belong to a compact set, which is the standing assumption in the existing literature. The motivation of this comes from considering a maximizing agent who is uncertain of the real-world measure but knows certain (linear) statistics of it, such as moments, probabilities or correlations pertaining the price process. We provide a full answer (attainability issues, min-max equality) in the complete market case, where we fix an Orlicz Space which permits to connect the properties of the uncertainty set to that of the utility function and its conjugate. Further we prove that the same approach never works beyond the complete market case, as the mentioned Orlicz Space has to be replaced by a Modular Space, which is not rich enough in the incomplete case. In the motivating set-up of linear statistics we apply general results of entropy minimization to give a new representation of the worst-case measure within the uncertainty set.