We present a theoretical framework for stressing multivariate stochastic models. We consider a stress to be a change of measure, placing a higher weight on multivariate scenarios of interest. In particular, a is a mapping from random vectors to Radon–Nikodym densities. We postulate desirable properties for stressing mechanisms addressing alternative objectives. Consistently with our focus on dependence, we require throughout invariance to monotonic transformations of risk factors. We study in detail the properties of two families of stressing mechanisms, based respectively on mixtures of univariate stresses and on transformations of statistics we call Spearman and Kendall’s cores. Furthermore, we characterize the aggregation properties of those stressing mechanisms, which motivate their use in deriving new capital allocation methods, with properties different to those typically found in the literature. The proposed methods are applied to stress testing and capital allocation, using the simulation model of a UK-based non-life insurer.

中文翻译：

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多元压力测试理论


我们提出了一个强调多元随机模型的理论框架。我们认为压力是衡量标准的改变，对感兴趣的多变量场景给予更高的权重。特别是，a 是从随机向量到 Radon-Nikodym 密度的映射。我们假设解决替代目标的压力机制具有理想的特性。与我们对依赖性的关注一致，我们要求风险因素始终保持单调变换的不变性。我们详细研究了两类压力机制的特性，分别基于单变量压力的混合和我们称为 Spearman 和 Kendall 核心的统计变换。此外，我们描述了这些压力机制的聚合属性，这促使它们用于推导新的资本配置方法，其属性与文献中通常发现的属性不同。使用英国非寿险公司的模拟模型，将所提出的方法应用于压力测试和资本配置。