Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 160, Issue 1-2, Pages 391-427Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-013-0531-y
Keywords
European options; Robust hedging; Min-max theorems; Prokhorov metric; Optimal transport
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Funding
- European Research Council [228053-FiRM]
- ETH Foundation
- Swiss Finance Institute
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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.
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