Before revision:  As a by-product, we recover the property that the Valloissolutions to the Skorokhod embedding problem (SEP) maximize and minimize the expectation of any convex function of the local time. 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 SEP as a generalization of the Vallois embedding .
After revision:  As a by-product, the optimality of Vallois' Skorokhod embeddings is recovered. In addition, under appropriate conditions, we derive a new solution to the two-marginal SEP as a generalization of the Vallois embedding .