The application of accumulation tests in Peaks-Over-Threshold modeling with Norwegian Fire insurance Data

TL;DR

This paper explores the use of accumulation tests combined with the Anderson-Darling test to select thresholds in Peaks-Over-Threshold modeling, improving the estimation of high quantiles in insurance data.

Contribution

It introduces a novel threshold selection method using accumulation tests in the POT framework, enhancing the modeling of excess insurance claims.

Findings

Accumulation tests effectively determine thresholds for GPD fitting.

The method yields accurate confidence intervals for Value-at-Risks.

Performance surpasses traditional graphical threshold selection methods.

Abstract

Modeling excess remains to be an important topic in insurance data modeling. Among the alternatives of modeling excess, the Peaks Over Threshold (POT) framework with Generalized Pareto distribution (GPD) is regarded as an efficient approach due to its flexibility. However, the selection of an appropriate threshold for such framework is a major difficulty. To address such difficulty, we applied several accumulation tests along with Anderson-Darling test to determine an optimal threshold. Based on the selected thresholds, the fitted GPD with the estimated quantiles can be found. We applied the procedure to the well-known Norwegian Fire Insurance data and constructed the confidence intervals for the Value-at-Risks (VaR). The accumulation test approach provides satisfactory performance in modeling the high quantiles of Norwegian Fire Insurance data compared to the previous graphical methods.