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 ⊆ C[0 , T] , where the superhedging property needs to hold pathwise, but only for paths lying in Ξ. For any Borel-measurable claim ξ bounded from below, the superhedging price coincides with the supremum over all pricing functionals E_Q[ξ] with respect to martingale measures ℚ concentrated on the prediction set Ξ. This allows us to include beliefs about 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.