  Convex duality for two two different super--replication problems in a
continuous time financial market with proportional transaction cost is proved.
In this market, static hedging in a finite number of options, in addition to
usual dynamic hedging with the underlying stock, are allowed. The first one the
problems considered is the model--independent hedging that requires the
super--replication to hold for every continuous path. In the second one the
market model is given through a probability measure P and the inequalities are
understood P almost surely. The main result, using the convex duality, proves
that the two super--replication problems have the same value provided that P
satisfies the conditional full support property. Hence, the transaction costs
prevents one from using the structure of a specific model to reduce the
super--replication cost.
