A càdlàg rough path foundation for robust finance
利用粗糙路径理论，为随机伊藤积分提供路径基础，涵盖常见交易策略和金融市场模型，包括奈特不确定性下的情形，并验证了功能生成策略和Cover通用投资组合的适用性。
Abstract 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.