  We consider the problem of superhedging under volatility uncertainty for an
investor allowed to dynamically trade the underlying asset, and statically
trade European call options for all possible strikes with some given maturity.
This problem is classically approached by means of the Skorohod Embedding
Problem (SEP). Instead, we provide a dual formulation which converts the
superhedging problem into a continuous martingale optimal transportation
problem. We then show that this formulation allows us to recover previously
known results about lookback options. In particular, our methodology induces a
new proof of the optimality of Az\'{e}ma-Yor solution of the SEP for a certain
class of lookback options. Unlike the SEP technique, our approach applies to a
large class of exotics and is suitable for numerical approximation techniques.
