Evaluating Reserve Risk in a Regulatory Perspective

We propose statistical methods for estimating not only the moments but the whole distribution of Claims Development Results (CDR), which is a key variable in calculating economic capital for non-life insurance reserving risk. These methods allow us to provide estimates of the under-provisioning risk, or reserve risk, associated with each accident year and of the global reserve risk. These risks are measured by the Value at Risk of the opposite of the CDR. We carefully examine the impact of two kinds of potential mistakes : wrongly assuming normality of the variables of interest and ignoring updating of the estimates of the parameters appearing in the statistical model. We show that both kinds of error may lead to large underestimations of the risk and, therefore, of the economic capital for reserving risk. These findings seem particularly important in a regulatory perspective.