We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Pengs G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian...

We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility maximization in incomplete semimartingale-driven financial markets. Unlike in the lower- and upper-hedging problems, and somewhat unexpectedly,...

Optimal execution and trading algorithms rely on price impact models, like the propagator model, to quantify trading costs. Empirically, price impact is concave in trade sizes, leading to nonlinear models for which optimization problems are intractable and even qualitative properties such as...