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：我们提出一种新的方法,用于验证由保险应用程序驱动的现实世界经济情景。这种方法基于Chevyrev和Oberhauser(2022年)开发的统计测试,以签名和最大平均距离概念为基础。测试可以检查两个随机过程路径样本是否来自同一分布。我们的贡献是将这一测试应用于与股票价格和波动以及精算应用中通货膨胀模拟相关的各种一维随机过程。首先,我们用合成数据进行数字分析,以测量测试的统计能力,然后,我们用历史数据研究测试的能力,以区分几个实际模型。这些数字实验是在两个限制下进行的。我们考虑一个不对称的环境,用来比较大量模拟真实世界情景的样本,一个小样本,包括(或代表合成数据案例)的历史数据。我们经常考虑的每月时间步骤和2。我们把两种样本与实践中所使用的验证方法的一致,即测量测试过程的统计方法,也就是说,我们一般在使用这一历史模型时,要用一个边缘数据分布到这个历史模型。我们用两个样本的最近一个样本,我们用这个模型来展示这个历史模型的数值,我们用两个样本的最近一个模型来展示。