Robust Hedging with Proportional Transaction Costs

TL;DR

This paper establishes a duality framework for robust hedging of path-dependent European options in discrete markets with proportional transaction costs, linking it to a Monge-Kantorovich type optimization problem.

Contribution

It introduces a duality result connecting robust hedging with a Monge-Kantorovich problem under proportional transaction costs in a discrete setting.

Findings

Duality between hedging and a transport optimization problem.

Characterization of optimal strategies under transaction costs.

Extension to path-dependent options with static and dynamic components.

Abstract

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Both the stock and the option trading is subject to proportional transaction costs. The main theorem is duality between hedging and a Monge-Kantorovich type optimization problem. In this dual transport problem the optimization is over all the probability measures which satisfy an approximate martingale condition related to consistent price systems in addition to the usual marginal constraints.