  We study superhedging of contingent claims with physical delivery in a
discrete-time market model with convex transaction costs. Our model extends
Kabanov's currency market model by allowing for nonlinear illiquidity effects.
We show that an appropriate generalization of Schachermayer's robust no
arbitrage condition implies that the set of claims hedgeable with zero cost is
closed in probability. Combined with classical techniques of convex analysis,
the closedness yields a dual characterization of premium processes that are
sufficient to superhedge a given claim process. We also extend the fundamental
theorem of asset pricing for general conical models.
