Martingale optimal transport and robust hedging in continuous time

• 成果类型: Article
• 署名作者: Dolinsky, Yan; Soner, H. Mete
• 署名单位: Hebrew University of Jerusalem; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0531-y
• 发表日期: 2014
• 页码: 391-427
• 关键词: CONTINGENT CLAIMS; Duality

摘要

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.