Utility maximization with a shortfall risk constraint under model uncertainty

In the utility maximization theory under model uncertainty one usually aims at maximizing a robust expected utility functional over affordable contingent claims Here we want to add the constraint of bounded robust shortfall risk induced by a convex loss function and a set of subjective measures which may differ from the set of measures in the definition of the robust expected utility functional. We will give a characterization of the solution to this constrained utility maximization problem by means of its dual problem.