Martingale transport, Skorokhod embedding and peacocks

A peacock is a continuous time stochastic process non-decreasing in convex ordering. A process is a peacock if and only if there is a martingale which has the same one-dimensional marginal distributions. Here we are interested in studying the ''extremal'' martingale associated to a given peacock. We will dicuss some results obtained by the martingale transport approach and the Skorokhod embedding approach.