  The Skorokhod embedding problem aims to represent a given probability measure
on the real line as the distribution of Brownian motion stopped at a chosen
stopping time. In this paper, we consider an extension of the optimal Skorokhod
embedding problem to the case of finitely-many marginal constraints. Using the
classical convex duality approach together with the optimal stopping theory, we
obtain the duality results which are formulated by means of probability
measures on an enlarged space. We also relate these results to the problem of
martingale optimal transport under multiple marginal constraints.
