Martingale Optimal Transport and Robust Hedging in Continuous Time

Yan Dolinsky and Halil Mete Soner
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Yan Dolinsky: ETH Zürich
Halil Mete Soner: ETH Zürich; Swiss Finance Institute

No 13-13, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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, fi xed 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: European Options; Robust Hedging; Min-Max Theorems; Prokhorov Metric; Optimal transport (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2013-04
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1313

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