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.

中文翻译：

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预测集上的路径式对冲

在本文中，我们针对预测集合\（\ Xi \ subseteq C [0，T] \）提供了与模型无关的对冲价格的定价对冲对偶，其中，对冲属性需要沿路径保持，但仅用于位于\（\ Xi \）中的路径。对于任何波雷尔可测量权利要求\（\ XI \）为下界限，与上确界在所有定价函的superhedging价格一致\（\ mathbb {E} _ {\ mathbb {Q}} [\Ⅺ] \）相对于mar措施measures集中在预测集\（\ Xi \）上。这使我们能够包含关于由集合\（\ Xi \）表示的价格过程的未来路径的信念，同时消除所有被视为不可能的内容。此外，我们提供了一些示例来证明我们的设置合理。