Pathwise super-replication via Vovk's outer measure

TL;DR

This paper develops a general duality framework for model-independent super-replication of various exotic derivatives using Vovk's outer measure, connecting robust pricing with the Skorokhod embedding problem.

Contribution

It introduces a new model-independent super-replication theorem in continuous time based on Vovk's approach, applicable to a wide class of derivatives.

Findings

Established a pricing-hedging duality for derivatives using finitely many marginals.

Derived a super-replication theorem covering lookback, Asian, and variance options.

Extended the robust finance framework to a broader set of exotic derivatives.

Abstract

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk's approach to mathematical finance we derive a model-independent super-replication theorem in continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely monitored Asian options, and options on realized variance.