  We consider the computation of model-free bounds for multi-asset options in a
setting that combines dependence uncertainty with additional information on the
dependence structure. More specifically, we consider the setting where the
marginal distributions are known and partial information, in the form of known
prices for multi-asset options, is also available in the market. We provide a
fundamental theorem of asset pricing in this setting, as well as a superhedging
duality that allows to transform the maximization problem over probability
measures in a more tractable minimization problem over trading strategies. The
latter is solved using a penalization approach combined with a deep learning
approximation using artificial neural networks. The numerical method is fast
and the computational time scales linearly with respect to the number of traded
assets. We finally examine the significance of various pieces of additional
information. Empirical evidence suggests that "relevant" information, i.e.
prices of derivatives with the same payoff structure as the target payoff, are
more useful that other information, and should be prioritized in view of the
trade-off between accuracy and computational efficiency.
