We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of \(d\) risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path-dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures. The superhedging problem is formulated with simple trading strategies, the claim is the limit inferior of continuous functions, which allows upper and lower semi-continuous claims, and superhedging is required in the pathwise sense on a \(\sigma \)-compact sample space of price trajectories. If the sample space is stable under stopping, the probabilistic problem reduces to finding the supremum over all martingale measures with compact support. As an application of the general results, we deduce dualities for Vovk’s outer measure and semi-static superhedging with finitely many securities.

中文翻译：

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连续时间中路径对冲的对偶

我们提供无模型定价-连续时间对冲对冲。对于由 具有连续价格轨迹的\（d \）风险资产组成的无摩擦市场，我们表明，找到路径依赖的欧式期权的最小对冲价格的纯粹分析问题与发现价格区间的纯粹概率问题具有相同的价值。在所有mar措施中，对期权的期望最高。超级套期保值问题是通过简单的交易策略制定的，索赔是连续函数的极限劣势，允许上下半连续索赔，并且在\（\ sigma \）上以顺向方式需要超级套期保值。-缩小价格轨迹的样本空间。如果样本空间在停止状态下是稳定的，则概率问题将减少到在紧凑支持下找到所有mar措施的最高点。作为一般结果的应用，我们推导了Vovk的外部度量和有限数量的有价证券半静态对冲的对偶性。