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|Abstract:||© 2013, Springer-Verlag Berlin Heidelberg. 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 have a 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.|
|Citation:||Dolinsky, Y, Soner, HM. (2013). Martingale optimal transport and robust hedging in continuous time. Probability Theory and Related Fields, 160 (1-2), 391 - 427. doi:10.1007/s00440-013-0531-y|
|Pages:||391 - 427|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Probability Theory and Related Fields|
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