We prove a robust super-hedging duality result for path-dependent options on assets with jumps in a continuous-time setting. It requires that the collection of martingale measures is rich enough and that the payoff function satisfies some continuity property. It is a by-product of a quasi-sure version of the optional decomposition theorem, which can also be viewed as a functional version of Itô’s lemma that applies to non-smooth functionals (of càdlàg processes) which are concave in space and nonincreasing in time, in the sense of Dupire.

中文翻译：

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Skorokhod 空间上的准确定可选分解和超对冲结果

我们证明了在连续时间设置中具有跳跃的资产的路径依赖期权的强大的超级对冲二元性结果。它要求马丁格尔测度的集合足够丰富，并且支付函数满足某种连续性。它是可选分解定理的准确定版本的副产品，它也可以被视为适用于非光滑泛函（càdlàg 过程的）的伊藤引理的泛函版本，这些泛函在空间上是凹的并且在时间，在杜皮尔的意义上。