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

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