In this paper, we investigate a path-dependent American option problem and provide an efficient and implementable numerical scheme for the solution of its associated path-dependent variational inequality. We obtain the viscosity characterization of our value function and suggest a monotone, stable and consistent numerical scheme, the convergence of which is proven thanks to the uniqueness property. We further enrich our study by providing and implementing a numerical algorithm. Some numerical results are also included.

中文翻译：

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路径依赖的美式期权

在本文中，我们研究了一个依赖于路径的美式期权问题，并为其相关的依赖于路径的变分不等式的解提供了一种有效且可实现的数值方案。我们获得了我们的价值函数的粘度特征，并提出了一个单调、稳定和一致的数值方案，由于唯一性，证明了其收敛性。我们通过提供和实施数值算法进一步丰富了我们的研究。还包括一些数值结果。