Martingale optimal transport and robust hedging in continuous time

Yan Dolinsky, H. Mete Soner

Research output: Contribution to journalArticle

81 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)391-427
Number of pages37
JournalProbability Theory and Related Fields
Volume160
Issue number1-2
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • European options
  • Min–max theorems
  • Optimal transport
  • Prokhorov metric
  • Robust hedging

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