Severity Modeling of Extreme Insurance Claims for Tariffication

28 Pages Posted: 10 May 2018 Last revised: 25 Aug 2018

See all articles by Christian Laudagé

Christian Laudagé

Fraunhofer ITWM - Department Financial Mathematics

Sascha Desmettre

University of Kaiserslautern - Department of Mathematics

Jörg Wenzel

Fraunhofer ITWM

Date Written: August 23, 2018

Abstract

Generalized linear models are common instruments for the pricing of non-life 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 peaks-over-threshold 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 the corresponding concrete log-likelihood functions above and below the threshold. Moreover, in the presence of extreme claims, we demonstrate the superiority of the threshold severity model compared to the commonly used generalized linear model based on the gamma distribution by a simulation study.

Keywords: extreme claims, generalized linear model, truncated gamma distribution, extreme value theory, peaks-over-threshold, generalized Pareto distribution

JEL Classification: C24, G22

Suggested Citation

Laudagé, Christian and Desmettre, Sascha and Wenzel, Jörg, Severity Modeling of Extreme Insurance Claims for Tariffication (August 23, 2018). Available at SSRN: https://ssrn.com/abstract=3168441 or http://dx.doi.org/10.2139/ssrn.3168441

Christian Laudagé (Contact Author)

Fraunhofer ITWM - Department Financial Mathematics ( email )

Fraunhofer-Platz 1
Kaiserslautern, 67663
Germany

Sascha Desmettre

University of Kaiserslautern - Department of Mathematics ( email )

Kaiserslautern, 67663
Germany

HOME PAGE: http://www.mathematik.uni-kl.de/~desmettre

Jörg Wenzel

Fraunhofer ITWM ( email )

Fraunhofer-Platz 1
Kaiserslautern, 67663
Germany

HOME PAGE: http://https://www.itwm.fraunhofer.de/de/abteilungen/fm.html

Register to save articles to
your library

Register

Paper statistics

Downloads
67
rank
323,381
Abstract Views
268
PlumX Metrics