We propose a new approach for the validation of real-world economic scenarios motivated by insurance applications. This approach is based on the statistical test developed by Chevyrev and Oberhauser (2022) and relies on the notions of signature and maximum mean distance. This test allows to check whether two samples of stochastic processes paths come from the same distribution. Our contribution is to apply this test to a variety of one-dimensional stochastic processes relevant for the modelling of equity stock price and volatility as well as inflation in view of actuarial applications. At first, we present a numerical analysis with synthetic data in order to measure the statistical power of the test and then, we work with historical data to study the ability of the test to discriminate between several models in practice. These numerical experiments are conducted under two constraints:1. we consider an asymmetric setting in which we compare a large sample of simulated real-world scenarios and a small sample that consists of (or represents in the synthetic data case) historical data, both with a monthly time step as often considered in practice and2. we make the two samples identical from the perspective of validation methods used in practice, i.e. we impose that the marginal distributions of the two samples are the same or very close at a given one-year horizon.By performing specific transformations of the signature, we obtain statistical powers close to 1 in this framework. Moreover, we show that some models are rejected and others are not when applying the test against historical data. These numerical results demonstrate the potential of this validation approach for real-world economic scenarios and more generally for any application requiring to exhibit the consistency of a stochastic model with historical paths. We also discuss several challenges related to the numerical implementation of this approach, and highlight its domain of validity in terms of the distance between models and the volume of data at hand.

翻译：我们提出了一种受保险应用驱动的新方法，用于验证真实经济场景。该方法基于Chevyrev和Oberhauser（2022）开发的统计检验，并依赖于签名（signature）和最大均值距离（maximum mean distance）的概念。该检验能够判断两组随机过程路径样本是否来自同一分布。我们的贡献在于，将此检验应用于多种一维随机过程，这些过程涉及权益股价、波动率及通货膨胀的建模，以服务于精算应用。首先，我们通过合成数据进行数值分析以衡量检验的统计功效，随后利用历史数据研究该检验在实际中区分不同模型的能力。这些数值实验在两项约束下进行：1）我们考虑非对称设置——将包含大量模拟真实场景的样本与仅包含（或在合成数据情况下代表）历史数据的小样本进行比较，且两者均采用实际中常用的月度时间步长；2）我们使这两个样本在实践验证方法视角下保持一致，即强制两个样本在给定一年期内的边际分布相同或极其接近。通过对签名执行特定变换，我们在此框架下获得了接近1的统计功效。此外，应用该检验于历史数据时，结果显示部分模型被拒绝而其他模型未被拒绝。这些数值结果证明了该验证方法在真实经济场景中的潜力，更广泛而言，适用于任何需展示随机模型与历史路径一致性的应用场景。我们还讨论了该方法数值实现中的若干挑战，并强调了其在模型间距离与可用数据量方面的有效性范围。