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Friday, July 7 • 11:00am - 11:18am

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Keywords: extreme value theory, censoring, splicing, risk measures
Webpages: https://CRAN.R-project.org/package=ReIns, https://github.com/TReynkens/ReIns
Reinsurance is an insurance purchased by one party (usually an insurance company) to indemnify parts of its underwritten insurance risk. The company providing this protection is then the reinsurer. A typical example of a reinsurance is an excess-loss insurance where the reinsurer indemnifies all losses above a certain threshold that are incurred by the insurer. Albrecher, Beirlant, and Teugels (2017) give an overview of reinsurance forms, and its actuarial and statistical aspects: models for claim sizes, models for claim counts, aggregate loss calculations, pricing and risk measures, and choice of reinsurance. The ReIns package, which complements this book, contains estimators and plots that are used to model claim sizes. As reinsurance typically concerns large losses, extreme value theory (EVT) is crucial to model the claim sizes. ReIns provides implementations of classical EVT plots and estimators (see e.g. Beirlant et al. 2004) which are essential tools when modelling heavy-tailed data such as insurance losses.
Insurance claims can take long before being completely settled, i.e. there is a long time between the occurrence of the claim and the final payment. If the claim is notified to the (re)reinsurer but not completely settled before the evaluation time, not all information on the final claim amount is available, and hence censoring is present. Several EVT methods for censored data are included in ReIns.
A global fit for the distribution of losses is e.g. needed in reinsurance. Modelling the whole range of the losses using a standard distribution is usually very hard and often impossible. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body, i.e. light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. Reynkens et al. (2016) propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. ReIns contains the implementation of the expectation maximisation (EM) algorithm to fit the splicing model to censored data. Risk measures and excess-loss insurance premiums can be computed using the fitted splicing model.
In this talk, we apply the plots and estimators, available in ReIns, to model real life insurance data. Focus will be on the splicing modelling framework and other methods adapted for censored data.
References Albrecher, Hansjörg, Jan Beirlant, and Jef Teugels. 2017. Reinsurance: Actuarial and Statistical Aspects. Wiley, Chichester.

Beirlant, Jan, Yuri Goegebeur, Johan Segers, and Jef Teugels. 2004. Statistics of Extremes: Theory and Applications. Wiley, Chichester.

Reynkens, Tom, Roel Verbelen, Jan Beirlant, and Katrien Antonio. 2016. “Modelling Censored Losses Using Splicing: A Global Fit Strategy with Mixed Erlang and Extreme Value Distributions.” https://arxiv.org/abs/1608.01566.

Speakers
TR

## Tom Reynkens

Friday July 7, 2017 11:00am - 11:18am CEST
2.02 Wild Gallery