Before revision:  The superhedging portfolio consists of {\it   static positions in liquidly traded vanilla  options, and a dynamic trading strategy , subject to certain constraints, on the risky asset. By the theory of Monge-Kantorovich  optimal transport, we establish a  superhedging duality, which admits a natural connection to convex risk measures.
After revision:  The superhedging portfolio consists of {\it static positions in liquidly traded vanilla options, and a dynamic trading strategy in risky assets under certain constraints. By considering the limit order book of each tradable exotic option and employing the Monge-Kantorovich optimal transport, we establish a superhedging duality, which admits a natural connection to convex risk measures.