Pathwise superhedging on prediction sets

TL;DR

This paper establishes a duality for model-independent superhedging prices constrained to a prediction set, linking pathwise hedging with martingale measures focused on plausible future paths.

Contribution

It introduces a novel duality framework for superhedging that incorporates prediction sets, allowing for pathwise pricing aligned with beliefs about future market behavior.

Findings

Superhedging price equals supremum over martingale measures on the prediction set

Framework accommodates beliefs about future paths, excluding impossible scenarios

Provides examples justifying the prediction set approach

Abstract

In this paper we provide a pricing-hedging duality for the model-independent superhedging price with respect to a prediction set $\Xi\subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in $\Xi$. For any Borel measurable claim $\xi$ which is bounded from below, the superhedging price coincides with the supremum over all pricing functionals $\mathbb{E}_{\mathbb{Q}}[\xi]$ with respect to martingale measures $\mathbb{Q}$ concentrated on the prediction set $\Xi$. This allows to include beliefs in future paths of the price process expressed by the set $\Xi$, while eliminating all those which are seen as impossible. Moreover, we provide several examples to justify our setup.