Three-level modelling of automobile insurance claim components for Manila data

This paper uses a three-level model to analyze policyholder claims on automobile insurance data. The three levels are claim frequency, claim type, and claim severity. In the first level, the negative binomial regression models were used to model count data. Using Akaike Information Criterion, Schwarz Bayesian Criterion, and total absolute difference, the results showed that negative binominal with p=2 gives the best fit. In level 2, two types of claims were considered. These are own damage (OD) and third party (TP). Binary logistics was used and the backward selection procedure gave the best results. In level 3, modeling claim severity, the gamma distribution and generalized beta of the second kind (GB2) were used. For OD claim type, mixed distribution was utilized and for TP, the usual modeling technique was applied. Under GB2, three approaches were considered. Based on the output, it can be seen that the second approach of GB2 provided the best fit for both claim types. However, the coefficient of determination achieved for both models are not that high, that is 60.74% for OD and 67.93% for TP respectively