The application of accumulation tests in peaks over threshold modeling with fire insurance data sets

Modeling excesses remains to be an important topic in insurance data modeling. Among the alternatives to modeling excess, the Peaks Over Threshold (POT) framework with Generalized Pareto distribution (GPD) is regarded as an efficient approach due to its flexibility. However, selecting an appropriate threshold for such a framework is a major difficulty. To address such difficulty, we applied several accumulation tests along with Anderson-Darling test to determine an optimal threshold. Limited simulations were conducted to assess the performance of accumulation tests. Based on the selected thresholds, the fitted GPD with the estimated quantiles can be found. We applied the procedure to the wellknown Norwegian fire insurance data and AON Re Belgian fire loss data. With the selected thresholds, confidence intervals for the Value-at-Risks (VaR) were constructed correspondingly. The accumulation test approach provides satisfactory performance in modeling the VaR of both data sets compared to the previous graphical methods.