LAUSR

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