Statistics of Extremes for the Insurance Industry

Battle Count: 52

While the paper is primarily focused on insurance and reinsurance applications, the extreme value theory techniques (Pareto-type modelling, Hill estimation, POT methodology, VaR/CTE estimation, multivariate extremes, copula-based dependence) are directly transferable to quantitative trading contexts. Tail risk management, portfolio stress testing, and derivative pricing for extreme events share methodological foundations. However, the specific adaptations (truncation from policy limits, tempering from claim management, censoring from IBNR/RBNS) are insurance-specific. The multivariate and spatial dependence modelling for catastrophes has limited direct trading application.

The paper covers a wide range of specialized EVT methods. Basic Hill estimation and Pareto QQ-plots are straightforward. However, truncated/tempered Pareto estimation, censored data methods (Kaplan-Meier adapted estimators), mixed Erlang fitting via EM algorithm, splicing model construction, multivariate GPD with Pickands dependence function estimation, and max-stable process fitting for spatial extremes all require significant statistical expertise and careful implementation. The EM algorithm for ME distributions, backward stepwise model selection, and numerical integration for multivariate premiums add further complexity.

The paper is a survey/review with illustrative examples. Some datasets are publicly available (Loss, ALAE from R package 'copula'; Norwegian fire insurance data referenced in literature). German flood data from MunichRe NatCatSERVICE is proprietary. Mathematical formulations and estimators are clearly presented, but full implementation code is not provided. The EM algorithm and splicing procedures are described algorithmically but would require significant implementation effort.