A Data‐Analytic Method for Forecasting Next Record Catastrophe Loss

We develop in this article a data‐analytic method to forecast the severity of next record insured loss to property caused by natural catastrophic events. The method requires and employs the knowledge of an expert and accounts for uncertainty in parameter estimation. Both considerations are essential for the task at hand because the available data are typically scarce in extreme value analysis. In addition, we consider three‐parameter Gamma priors for the parameter in the model and thus provide simple analytical solutions to several key elements of interest, such as the predictive moments of record value. As a result, the model enables practitioners to gain insights into the behavior of such predictive moments without concerning themselves with the computational issues that are often associated with a complex Bayesian analysis. A data set consisting of catastrophe losses occurring in the United States between 1990 and 1999 is analyzed, and the forecasts of next record loss are made under various prior assumptions. We demonstrate that the proposed method provides more reliable and theoretically sound forecasts, whereas the conditional mean approach, which does not account for either prior information or uncertainty in parameter estimation, may provide inadmissible forecasts.