Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach

David LEE, Wai Keung LI, Tony Siu Tung WONG

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We consider a model which allows data-driven threshold selection in extreme value analysis. A mixture exponential distribution is employed as the thin-tailed distribution in view of the special structure of insurance claims, where individuals are often grouped into categories. An EM algorithm-based procedure is described in model fitting. We then demonstrate how a multi-level fitting procedure will substantially reduce computation time when the data set is large. The fitted model is applied to derive statistics such as return level and expected tail loss of the claim distribution, and ruin probability bounds are obtained. Finally we propose a statistical test to justify the choice of mixture exponential distribution over the homogeneous exponential distribution in terms of improved fit. Copyright © 2012 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)538-550
JournalInsurance: Mathematics and Economics
Volume51
Issue number3
Early online dateJul 2012
DOIs
Publication statusPublished - Nov 2012

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Peaks over Threshold
Exponential Model
Exponential distribution
Mixture Model
Insurance
Mixture Distribution
Modeling
Probability Bounds
Ruin Probability
Model Fitting
Extreme Values
EM Algorithm
Statistical test
Data-driven
Justify
Tail
Statistics
Model
Demonstrate

Citation

Lee, D., Li, W. K., & Wong, T. S. T. (2012). Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach. Insurance: Mathematics and Economics, 51(3), 538-550. doi: 10.1016/j.insmatheco.2012.07.008

Keywords

  • Mixture exponential distribution
  • Extreme value theory
  • Threshold model
  • Mixture component testing
  • Insurance claims modeling