Pathwise superhedging on prediction sets

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.