Hedging of claims with physical delivery under convex transaction costs

TL;DR

This paper investigates superhedging of claims with physical delivery in markets with convex transaction costs, extending existing models to include nonlinear illiquidity effects and providing dual characterizations of superhedging prices.

Contribution

It generalizes Kabanov's currency market model by incorporating nonlinear illiquidity effects and extends the fundamental theorem of asset pricing to conical models with convex transaction costs.

Findings

Set of hedgeable claims with zero cost is closed in probability.

Provides a dual characterization of superhedging premium processes.

Extends the fundamental theorem of asset pricing to convex transaction cost models.

Abstract

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.