Using rough path theory, we provide a pathwise foundation for stochastic Itô integration which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called property (RIE) for càdlàg paths, which is shown to imply the existence of a càdlàg rough path and of quadratic variation in the sense of Föllmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Cover’s universal portfolio are admissible integrands, and that property (RIE) is satisfied by both (Young) semimartingales and typical price paths.

使用粗糙路径理论，我们为随机 Itô 积分提供了路径基础，涵盖了金融市场最常用的交易策略和数学模型，包括奈特不确定性下的策略和数学模型。为此，我们引入了所谓的 càdlàg 路径属性（RIE），它表明存在 càdlàg 粗糙路径和 Föllmer 意义上的二次变分。我们证明了相应的粗积分作为左点黎曼和的极限沿着适当的分区序列存在。这允许我们处理非梯度类型的被积函数，并提供粗糙路径理论强大的稳定性估计。此外，我们验证（路径相关）函数生成的交易策略和 Cover 的通用投资组合是可接受的被积函数，并且（年轻）半鞅和典型价格路径都满足属性 (RIE)。