Robust hedging and pathwise calculus

TL;DR

This paper compares two pathwise hedging methods, showing they produce identical strategies when both exist, and extends robustness results from one method to the other.

Contribution

It establishes the equivalence of BSV and CF pathwise hedging approaches and proves a robust replication result for CF strategies.

Findings

Both approaches yield the same hedging strategies when both exist.

BSV type robust replication results hold for CF strategies.

The paper bridges two different pathwise hedging frameworks.

Abstract

We study the connections of two different pathwise hedging approaches. These approaches are BSV by Bender-Sottinen-Valkeila and CF by Cont-Fourni\'e. We prove that both approaches give the same pathwise hedges, whenever both of the strategies exist. We also prove BSV type robust replication result for CF strategies.