Martingale Optimal Transport and Robust Hedging in Continuous Time

TL;DR

This paper establishes a duality between robust hedging of path-dependent options and a martingale optimal transport problem, providing new theoretical insights and practical super-replication strategies in continuous-time financial markets.

Contribution

It proves a duality result linking robust hedging with martingale optimal transport and constructs simple portfolios that asymptotically achieve minimal super-replication costs.

Findings

Duality between robust hedging and martingale optimal transport established.

Constructed portfolios asymptotically attain minimal super-replication cost.

Provided a framework for model-independent option pricing in continuous time.

Abstract

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.