Statistics of Extremes for the Insurance Industry

2025/11/27 by Albrecher, Hansjoerg, Beirlant, Jan
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Economics and business #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Probability and Risk Models #Risk Management (q-fin.RM) #Statistical Distribution Estimation and Applications

paper · doi:10.48550/arxiv.2511.22272

openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We provide a survey of how techniques developed for the modelling of extremes naturally matter in insurance, and how they need to and can be adapted for the insurance applications. Topics covered include truncation, tempering, censoring and regression techniques. The discussed techniques are illustrated on concrete data sets.

Citations

• Censored extreme value estimation
• Bayesian modeling of insurance claims for hail damage
• Informed censoring: the parametric combination of data and expert information
• Expert Kaplan--Meier estimation
• Heavy-tailed phase-type distributions: A unified approach
• Trimmed extreme value estimators for censored heavy-tailed data
• Sparse Structures for Multivariate Extremes
• Tempered Pareto-type modelling using Weibull distributions
• Multivariate Matrix Mittag--Leffler distributions
• Multivariate fractional phase--type distributions
• Modelling extreme claims via composite models and threshold selection methods
• Combined Tail Estimation Using Censored Data and Expert Information
• Matrix Mittag--Leffler distributions and modeling heavy-tailed risks
• Trends in the extremes of environments associated with severe US\n thunderstorms
• Estimation of the extreme value index in a censorship framework: asymptotic and finite sample behaviour
• Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications
• Regression Type Models for Extremal Dependence
• Tail fitting for truncated and non-truncated Pareto-type distributions

Related

• Modeling extreme values by the residual coefficient of variation
• Threshold selection and trimming in extremes
• Extreme value analysis of actuarial risks: estimation and model\n validation
• Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications
• An Intuitive Curve-Fit Approach to Probability-Preserving Prediction of\n Extremes