标题： 基于最小最大算法的路径依赖期权的稳健对冲 显示英文标题

标题： Robust Hedging of path-dependent options using a min-max algorithm

摘要： 我们考虑一个投资者，他想使用现金、标的资产以及相同标的的到期日为$ t_1$的欧式看跌/看涨期权来构建一个静态对冲组合，以对冲一个到期日为$T$的路径依赖型期权，其中$0 < t_1 < T$。 我们提出了一种无模型的方法来构建这样的组合。 该框架受到\textit{对偶}鞅最优运输（MOT）问题的启发，该问题由\cite{beiglbock2013model}首创。 优化问题是确定一种组合构成，使得在$t_1$时预期最坏情况对冲误差最小（这与用于对冲组合的期权的到期日一致）。 最坏情况对应于导致最差对冲表现的分布。 这种表述导致了一个\textit{极小极大}问题。 当有有限数量的欧式期权价格可用时，我们提供了一个求解该问题的数值方案。 该模型无关方法在期权价格使用\textit{布莱克-舒尔斯}和\textit{默顿跳扩散}模型生成时的对冲性能的数值结果如上所示。 我们还提供了在$T$，即目标期权到期日的对冲误差理论边界。 显示英文摘要

摘要： We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$. We propose a model-free approach to construct such a portfolio. The framework is inspired by the \textit{primal-dual} Martingale Optimal Transport (MOT) problem, which was pioneered by \cite{beiglbock2013model}. The optimization problem is to determine the portfolio composition that minimizes the expected worst-case hedging error at $t_1$ (that coincides with the maturity of the options that are used in the hedging portfolio). The worst-case scenario corresponds to the distribution that yields the worst possible hedging performance. This formulation leads to a \textit{min-max} problem. We provide a numerical scheme for solving this problem when a finite number of vanilla option prices are available. Numerical results on the hedging performance of this model-free approach when the option prices are generated using a \textit{Black-Scholes} and a \textit{Merton Jump diffusion} model are presented. We also provide theoretical bounds on the hedging error at $T$, the maturity of the target option.