Sensitivity analysis with χ2-divergences

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 χ2-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 χ2- and the Kullback-Leibler divergence, indicating that the former can be evaluated with lower sampling error.