Duality for pathwise superhedging in continuous time

Daniel Bartl, Michael Kupper, David J. Prömel, Ludovic Tangpi

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of d risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path-dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures. The superhedging problem is formulated with simple trading strategies, the claim is the limit inferior of continuous functions, which allows upper and lower semi-continuous claims, and superhedging is required in the pathwise sense on a σ-compact sample space of price trajectories. If the sample space is stable under stopping, the probabilistic problem reduces to finding the supremum over all martingale measures with compact support. As an application of the general results, we deduce dualities for Vovk’s outer measure and semi-static superhedging with finitely many securities.

Original languageEnglish (US)
Pages (from-to)697-728
Number of pages32
JournalFinance and Stochastics
Volume23
Issue number3
DOIs
StatePublished - Jul 15 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Keywords

  • Martingale measures
  • Pathwise superhedging
  • Pricing–hedging duality
  • Semi-static hedging
  • Vovk’s outer measure
  • σ-compactness

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