  We introduce an efficient computational framework for solving a class of
multi-marginal martingale optimal transport problems, which includes many
robust pricing problems of large financial interest. Such problems are
typically computationally challenging due to the martingale constraint,
however, by extending the state space we can identify them with problems that
exhibit a certain sequential martingale structure. Our method exploits such
structures in combination with entropic regularisation, enabling fast
computation of optimal solutions and allowing us to solve problems with a large
number of marginals. We demonstrate the method by using it for computing robust
price bounds for different options, such as lookback options and Asian options.
