Abstract

Climate change is leading to an increase in the severity and prevalence of natural catastrophes. From a statistical and actuarial perspective, it is desirable to measure the potential impact of changes in different aspects of these extreme events. Sensitivity analysis is used to measure and characterize uncertainty of a model based on these changes, where a baseline model includes a number of covariates mapped to an output via an aggregation function. Given a defined stress on the baseline distribution, a type of sensitivity analysis used in actuarial mathematics, Reverse Sensitivity Testing, is suitable for several types of models (including black box models) and uses different risk measures along with the Kullback–Leibler divergence (KL divergence) as a measure of discrepancy between the baseline probability measure and the stressed probability measure. An expansion of Reverse Sensitivity Testing is provided to include both a coherent and elicitable risk measure; expectiles. Since the KL divergence is considered to be a pessimistic divergence for extreme values, the Renyi divergence, which is a broader divergence, is included as an extension ideal for extreme events given a user specified order parameter. Both the KL divergence and the Renyi divergence are implemented on a standard normal random variable, a numerical example, and then applied to extreme loss data from a natural catastrophe that hit Western Canada in 2020.