Motor Vehicle Third Party Liability Insurance Loss Frequency Models And Reward Systems

Automobile Third Party Liability Insurance has been run for a few years in our country and there are a wealth of experience claim data. Experience study that based on experience claim data takes an important role in actuarial research on property and casualty insurance. The most important content of risk management is to find reasonable claim frequency models.Zero claim frequency comes from three sources. The first is no accident happened, the second is an unreported claim after accident happened and the third is a disapproved claim. The zero observations that came from the second and third source are called extra zeros and the phenomenon is called zero-inflated in this paper. The source of extra zeros may come from the unreported claims due to deductible and bonus-malus system in Automobile Third Party Liability Insurance. One of important distinctive features of claim frequency data collected from Automobile Third Party Liability Insurance is zero inflated. Therefore traditional application of Poisson and Negative Binomial distribution for model fitting may not be adequate and dispersion appears.The purpose of this paper is to find proper models to fit claim data of our country and to do valuation research on bonus-malus system based on the best fitting model. This paper mainly focuses on selection of claim frequency models. Zero-inflated Poisson Mixed Regression Model and Zero-inflated Negative Binomial Mixed Regression Model with random effect are introduced.As a result of the study, the data of Automobile Third Party Liability Insurance in China is better fitted by Zero-inflated Mixed Regression Models which accommodate the extra zeros and the extra dispersion of data. Due to the regression models used, the level of risk of policies could be evaluated by covariates. The findings in this paper could make contribution to price of Automobile Third Party Liability Insurance and providing a new screen of valuation of bonus-malus system.