We introduce an approach to sensitivity analysis of quantitative risk models, for the purpose of identifying the most influential inputs. The proposed approach relies on a change of measure derived by minimising the ${\chi }^2$-divergence, subject to a constraint (‘stress’) on the expectation of a chosen random variable. We obtain an explicit solution of this optimisation problem in a finite space, consistent with the use of simulation models in risk management. Subsequently, we introduce metrics that allow for a coherent assessment of reverse (i.e. stressing the output and monitoring inputs) and forward (i.e. stressing the inputs and monitoring the output) sensitivities. The proposed approach is easily applicable in practice, as it only requires a single set of simulated input/output scenarios. This is demonstrated by application on a simple insurance portfolio. Furthermore, via a simulation study, we compare the sampling performance of sensitivity metrics based on the ${\chi }^2$- and the Kullback-Leibler divergence, indicating that the former can be evaluated with lower sampling error.

我们引入了一种定量风险模型敏感性分析的方法，目的是确定最具影响力的输入。建议的方法依赖于通过最小化${\chi }^2$-发散，受对所选随机变量的期望的约束（“压力”）。我们在有限空间中获得了该优化问题的显式解，这与在风险管理中使用模拟模型一致。随后，我们引入了允许对反向（即强调输出和监控输入）和正向（即强调输入并监控输出）敏感性进行连贯评估的指标。所提出的方法在实践中很容易应用，因为它只需要一组模拟输入/输出场景。这可以通过在简单的保险组合上的应用来证明。此外，通过模拟研究，我们比较了基于${\chi }^2$- 和 Kullback-Leibler 散度，表明前者可以以较低的抽样误差进行评估。