基于最优输运的配送模式风险量化
Quantifying Distributional Model Risk via Optimal Transport
摘要：
本文讨论了在计算一般期望值时模型误设定的影响的量化问题。我们提出的方法是适用的，在很大的普遍性，特别是，我们提供的例子涉及路径依赖的期望随机过程。我们的方法包括在计算边界的期望感兴趣的概率测度使用，只要测量位于规定的公差测量的灵活类的距离从一个合适的基线模型。这些距离，基于概率测度之间的最佳运输，包括Wasserstein距离作为特殊情况。所提出的方法是非常适合于风险分析，因为我们证明了一些应用程序。我们还讨论了如何估计非参数化的公差区域使用Skorokhod型嵌入在这些应用程序中的一些。
英文摘要：
This paper deals with the problem of quantifying the impact of model misspecification when computing general expected values of interest. The methodology that we propose is applicable in great generality, in particular, we provide examples involving path dependent expectations of stochastic processes. Our approach consists in computing bounds for the expectation of interest regardless of the probability measure used, as long as the measure lies within a prescribed tolerance measured in terms of a flexible class of distances from a suitable baseline model. These distances, based on optimal transportation between probability measures, include Wasserstein's distances as particular cases. The proposed methodology is well-suited for risk analysis, as we demonstrate with a number of applications. We also discuss how to estimate the tolerance region non-parametrically using Skorokhod-type embeddings in some of these applications.
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