Martingale Optimal Transport and Robust Hedging 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.
Keywords
Cite
@article{arxiv.1208.4922,
title = {Martingale Optimal Transport and Robust Hedging in Continuous Time},
author = {Yan Dolinsky and H. Mete Soner},
journal= {arXiv preprint arXiv:1208.4922},
year = {2013}
}