  We introduce a novel and highly tractable supervised learning approach based
on neural networks that can be applied for the computation of model-free price
bounds of, potentially high-dimensional, financial derivatives and for the
determination of optimal hedging strategies attaining these bounds. In
particular, our methodology allows to train a single neural network offline and
then to use it online for the fast determination of model-free price bounds of
a whole class of financial derivatives with current market data. We show the
applicability of this approach and highlight its accuracy in several examples
involving real market data. Further, we show how a neural network can be
trained to solve martingale optimal transport problems involving fixed marginal
distributions instead of financial market data.
