Pathwise superhedging on prediction sets

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 ) bounded from below, the superhedging price coincides with the supremum over all pricing functionals (mathbb{E}_{mathbb{Q}}[ xi ]) with respect to martingale measures ℚ concentrated on the prediction set (Xi ). This allows us to include beliefs about 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.