Hedging of Claims with Physical Delivery under Convex Transaction Costs

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.