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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Severity modeling of extreme insurance claims for tariffication
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Postprint urn:nbn:de:0011n5521609 (2.1 MByte PDF) MD5 Fingerprint: 421af1f01dfe43685b74942025de2381 Erstellt am: 19.7.2019 
 Insurance. Mathematics & economics 88 (2019), S.7792 ISSN: 01676687 

 Englisch 
 Zeitschriftenaufsatz, Elektronische Publikation 
 Fraunhofer ITWM () 
 Extreme claim; Generalized linear model; Truncated gamma distribution; Extreme value theory; Peaksoverthreshold; Generalized Pareto distribution 
Abstract
Generalized linear models are common instruments for the pricing of nonlife insurance contracts. They are used to estimate the expected frequency and severity of insurance claims. However, these models do not work adequately for extreme claim sizes. To accommodate for these extreme claim sizes, we develop the threshold severity model, that splits the claim size distribution in areas below and above a given threshold. More specifically, the extreme insurance claims above the threshold are modeled in the sense of the peaksoverthreshold methodology from extreme value theory using the generalized Pareto distribution for the excess distribution, and the claims below the threshold are captured by a generalized linear model based on the truncated gamma distribution. Subsequently, we develop th e corresponding concrete loglikelihood functions above and below the threshold. Moreover, in the presence of simulated extreme claim sizes following a lognormal as well as Burr Type XII distribution, we demonstrate the superiority of the threshold severity model compared to the commonly used generalized linear model based on the gamma distribution.