  In a discrete-time market, we study model-independent superhedging, while the
semi-static superhedging portfolio consists of {\it three} parts: static
positions in liquidly traded vanilla calls, static positions in other tradable,
yet possibly less liquid, exotic 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 theory of
optimal transport, we establish a general superhedging duality, which admits a
natural connection to convex risk measures. With the aid of this duality, we
derive a model-independent version of the fundamental theorem of asset pricing.
The notion "finite optimal arbitrage profit", weaker than no-arbitrage, is also
introduced. It is worth noting that our method covers a large class of Delta
constraints as well as Gamma constraint.
