Alexander Schied, Berlin University of Technology

Aspects of model uncertainty and robustness in finance and economics

Due to the complexity of financial price processes, their mathematical models are often subject to model misspecification. In this talk we present some recent results on the robustness of certain trading strategies with respect to model uncertainty. In the first part, we consider the robustness of the Delta hedging strategy of an exotic derivative with respect to realized volatility when the underlying model is a local volatility model. Our analysis is based on volatility comparison techniques for SDEs. In the second part, we focus on the construction of optimal investment strategies for an investor who is averse against both risk and model uncertainty. Here one can use or combine several techniques including convex duality, nonlinear PDEs, and robust statistical test theory. In some special cases, the problems considered in parts one and two are closely related to each other.