Düzenlenmiş Sözde-Kopula Regresyon Modeli
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Göster/ Aç
Tarih
2020Yazar
Erdemir, Övgücan Gönenç
Ambargo Süresi
Açık erişimÜst veri
Tüm öğe kaydını gösterÖzet
In non-life insurance calculations, the assumption that the claim severity and frequency
are independent is frequently used. Although the independence assumption greatly
simplifies many of the calculations, it is not very realistic, and it can often lead to over or
under estimation of quantities of interest. For this reason, the dependency should be
modeled and included in the calculations instead of the independence assumption. In this
thesis, it is aimed to analyse and model the dependency between the claim severity and
frequency in non-life insurance. For this purpose, the claim severity and the claim
frequency are modeled with marginal gamma and marginal Poisson generalized linear
models, respectively. By considering these generalized linear models together with the
modified pseudo-Gauss copula functions, the modified pseudo-copula regression model
is proposed. With the pseudo-copulas, close estimations to the real data are found, and
with the modified correlation coefficients, a flexible dependency modeling is presented
according to the dependency between the claim severity and frequency. The proposed
model is tested with both simulation and real data analysis. The efficiency of the
modification on the pseudo-copula function is analyzed under different scenarios with the
simulation study. In the real data analysis, in insurance portfolios where there is different
relationships between claim severity and frequency, the dependency between the claim
iv
severity and frequency is modeled with the modified pseudo-copula regression model.
The pseudo-maximization by parts method is used in the parameter estimation. Under the
assumption of independence and when dependency is taken into account, the mean square
errors of the parameter estimates according to different modifications are calculated and
compared. It is observed that the parameters estimated by the modified pseudo-copula
regression model have lower mean square error than the estimates found with the model
using the constant correlation coefficient and the model under the independence
assumption. Finally, the standard copula regression model and the modified pseudocopula
regression model are compared and it is observed that the proposed model give
better results.