Joscha Diehl Technische Universität Berlin We study equations that are driven by a deterministic rough path and an additional stochastic Brownian motion. These kind of equations appear in finance, previsible stochastic control and stochastic filtering. One mathematical interesting problem is their exponential integrability, which we prove using recent advances on this topic. This is joint work with Peter Friz, Harald Oberhauser and Sebastian Riedel.