Modelling non-life insurance in Sri Lanka using Cox Hazard Model and classification of risky customers

Abstract

Some of the major factors that help the decision-making process of an insurance company include Time of the first claim (TFC), claim Size and the frequency of claims. However, in most situations researchers focus mainly on the second and third factors mentioned above. We hypothesize the importance of the TFC of an insurance contract in the decision-making process. Empirical evidence of motor vehicle insurance data in Sri Lanka suggests that nine covariates are responsible for the claim sizes. In the current study, our main objective is to find the key factors of those nine that are responsible for the TFC of the insurance contract. This study is based on the claim data in the whole year of 2016 of non-life insurance policies of a particular insurance company in Sri Lanka. Considering the TFC as right-censored data, selected nonparametric methods, i.e., Kaplan-Meier, Nelson-Aalen estimators, and Cox Proportional Hazard Model are used to analyze the data. We identified the five most influential covariates namely, vehicle type, log of Premium Value and that of Assured Sum, the lease type and the age range via fitting the Cox Model to TFC data. After a thorough residual analysis, the Logistic regression model has been used to identify the important covariates to classify future customers as risky or not.

Key words: Classification, Cox Proportional Hazard model, Kaplan-Meier, Right-censored