Zip Hierarchical Claims Model Of Car Insurance Actuarial Applications

This article describes statistical modeling of detailed, micro-level automobile in-surance data. Compared with the traditional statistical tools which usually focus on portfolio-level, our model refers to experience at the individual level, such as vehicle type, No claim discount, insurance coverage and so on. Moreover, the claims expe-rience consist of the detailed information on the type of insurance claim, including whether the claim is due to a third party, property damage to a third party or damage to the insured, as well as the claim severity.Motivated by Frees and Valdez(2008), We propose the hierarchical model, cor-responding to the frequency, type and severity of different types claim. The first one is Zero inflated poisson model with random effect for assessing claim frequency given the excess number of "0" claim.The second is a discrete choices model to predict the type of insurance claim, whether it is third party injury, third party damage, insured's own damage or some combination.The last part is for claim severity.Here, we use one special type of generalized beta of the second kind whose distribution has long tail and normal copula to account for the dependance among different claim types.We also give an approximate equation for estimate the mean squared error of pre-diction(MSEP) to judge the prediction quality of our model. Using simulation, we demonstrate the integrated model predict automobile claims and severity in a very ef-ficient way. The model takes the complexity of real actuary data into consideration, as well as implementing flexible statistical methods and reasonable prediction strategy. It can provide one class of models with flexibility and robust prediction effect.