Before revision:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case . We provide a construction of two-marginal embedding and some examples for which the robust superhedging problem is solved .
After revision:  By using the stochastic control approach initiated by Galichon, Henry-Labordere and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois ' embeddings to the SEP . Furthermore, we extend the analysis to the two-marginal case , where we provide candidates for the optimal hedging strategies, and, we construct a new solution to the two-marginal embedding and some examples for which the robust superhedging problem is solved .