In this talk we study strongly robust optimal control problems under volatility uncertainty, i.e. in the case when the volatility of the underlying stochastic process is unknown. In this case we need to consider a family of different volatility processes instead of just one fixed process (and hence also a family of models related to them).
Volatility uncertainty has been investigated in the literature by following two approaches, i.e. by introducing an abstract sublinear expectation space with a special process called G-Brownian motion (see ), or by quasi-sure analysis (see ). Here we work in a G-Brownian motion setting as in  and use the related stochastic calculus.
In the G-framework we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongly robust optimal control, which is optimal not only in the worst case scenario, but also for all probability measures with respect to the chosen optimality criterion. We discuss and illustrate the results by considering several examples.
This talk is based on the joint work .
 F. Biagini, T. Meyer-Brandis, B. Øksendal, C. Paczka, “Optimal control with delayed information flow of systems driven by G-Brownian motion”, Preprint, LMU and University of Oslo, 2014.
 L. Denis and C. Martini, “A theoretical framework for the pricing of contingent claims in the presence of model uncertainty”, The Annals of Applied Probability, 16:827–852, 2006.
 S. Peng. G-expectation, “G-Brownian motion and related stochastic calculus of Itô type”, Stochastic Analysis and Applications, 2:541–567, 2007.