Ting (Iris) Zhang
Integer-Valued Autoregressive Processes with Dynamic Heterogeneity and their Applications in Automobile Insurance
Bonus-malus systems in automobile insurance describe how the past claim frequencies determine the future insurance premiums. For a portfolio of automobile policies, the potential risks of the policyholders vary among individuals due to differences in driving behaviour, which leads to the unobserved heterogeneity in individual average claim counts. While the Poisson distribution has been used as a simple model for discrete count data, the negative binomial distribution is suggested for modeling the claim counts with unobserved heterogeneity by letting the mean parameter of the Poisson distribution follow a Gamma distribution. In this thesis, we introduce an integer-valued autoregressive process with dynamic heterogeneity for modeling claim counts incurred by individual policies in consecutive years. This model reflects random fluctuations and correlations of the heterogeneity from year to year, as well as reasonable correlations among the lagged claim counts. Some properties of the model are derived, and a bonus-malus system is built and illustrated using the Gibbs Sampler algorithm. Finally, comparisons with other existing models in the literature are provided in terms of the extent to which they involve the information carried by claim history.