The impact of dependence between claim frequency and severity on expected loss using GLM: MTPL application

Date

2024-7-31

Author

Aslanöz, İlkyaz

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In non-life insurance, the accurate estimation of total loss is extremely important for companies' asset-liability management. To estimate the total loss, insurance companies use generalized linear model (GLM) as it is compatible with insurance data and hence makes considerably consistent predictions. The common practice is constructing a GLM for frequency, usually using the Poisson distribution, and another GLM for severity, usually using the Gamma distribution, and then multiplying the results of these two models. However, this multiplication is only possible under the assumption of independence of the claim frequency and severity. Although the independence assumption simplifies the modeling, it also causes deviations from the real loss value. In this thesis, constructing a GLM, which can incorporate the dependence between claim frequency and severity, to predict the total loss is aimed. Two GLMs are built and tested; dependent-GLM and copula-GLM, and they are compared with the regular independent-GLM. To examine these models, non-life motor third party liability (MTPL) insurance data is used. In the first model, the dependency is provided by taking the claim number as a covariate of marginal severity GLM. The second model provides the dependence between the marginal frequency and severity GLMs by using a copula function. To compare these two dependent models and the independent model, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are used, and also the means of the estimations of the models are compared to the means of the real observations. The findings show that the independent-GLM deviates more from the real value compared to the other two. On the other hand, the dependent-GLM model is quite close to the copula-GLM model but gives slightly better results.

Subject Keywords

Generalized linear model, Copula, Dependence, Claim frequency, Claim severity

URI

https://hdl.handle.net/11511/110847

Collections

Graduate School of Applied Mathematics, Thesis