Hayat Dışı Sigortalarda Hasar Modellemesini Etkileyen Faktörlerin Kantil Regresyon ile İncelenmesi

Abstract

Motor insurance, which is included in the non-life branch, constitutes a significant part of the insurance premiums produced in Turkey. Insurance companies operating in the non-life branch have to offer competitive prices compared to rival companies in order to underwrite policies in this field. This situation increases the importance of pricing, especially in motor insurance, by taking the insured's risk group into account.

Traditional models have disadvantages such as ignoring the interdependence of insured risks, lack of information on the adequacy of the selected model and insensitivity to extreme losses. However, it is important for competitive pricing to include the effects of all variables, including outliers, that affect the loss in the pricing of the insurance policy. At the same time, when insurance companies calculate premiums based on expected losses with traditional methods, they cannot differentiate premium loading according to the riskiness of the policy group by using risk loading factors at the same rate for all policy risk groups. Insurance companies should realize pricing in a way to include the impact of extreme values related to the risk group on policy pricing and reflect this risk in insurance premiums.

A two-stage quantile regression model is proposed to determine the pricing subjectively for risk groups. This model allows for estimation without ignoring situations where the values of extreme losses can be reflected in the risk, the dependency of the insured risks and the lack of information on the statistical adequacy of the selected model.

In this study, it is proposed to use two-stage quantile regression to examine the factors affecting loss modeling in the non-life insurance branch. In this context, logistic regression and two-stage quantile regression models are explained in detail and studies in the literature are mentioned. In the application phase of the study, an application of the two-stage quantile regression model is performed on the motor insurance claims data of a non-life insurance company for the year 2022 obtained from the Insurance Information and Surveillance Center (SBM). In the first stage of the analysis, the probabilities of occurrence and non-occurrence of the damage were calculated by logistic regression. In the second stage, a quantile regression model was applied for the cases where the loss was determined to have occurred. The premium amounts obtained according to the results of the expected value premium calculation method using a positive constant loading factor are compared with the premium amounts obtained by risk loading according to the quantile premium principle as a result of the two-stage quantile regression model and the results are interpreted. According to the results obtained from the two-stage quantile regression model, it was observed that the premium calculation based on the quantile premium principle allows for a more accurate and fairer premium calculation since it takes into account the risks of the insured and the loading rates are calculated by taking into account the riskiness levels.