  We consider robust pricing and hedging for options written on multiple assets
given market option prices for the individual assets. The resulting problem is
called the multi-marginal martingale optimal transport problem. We propose two
numerical methods to solve such problems: using discretisation and linear
programming applied to the primal side and using penalisation and deep neural
networks optimisation applied to the dual side. We prove convergence for our
methods and compare their numerical performance. We show how adding further
information about call option prices at additional maturities can be
incorporated and narrows down the no-arbitrage pricing bounds. Finally, we
obtain structural results for the case of the payoff given by a weighted sum of
covariances between the assets.
