Statistical modelling of insurance claims

© 2013 Dr. Qing LiuThis PhD thesis consists of four main chapters that are based on the research outputs from three research projects. All of these projects focus on statistical modelling of insurance claims data, however, the data sets used (real world insurance claims data from various insurance providers) are not related to each other. As a result, the last three chapters are all self-supported and could be fully understood without referring to each other. Chapter two presents a nonparametric method for modelling a set of automobile insurance claims data which contains two dimensional claim costs. A Markov chain Monte Carlo (MCMC) simulation algorithm is developed for estimating parameters in the kernel density estimation of this claims data via transformations. The Bayesian sampling algorithm is employed and an approach is proposed to estimating the bandwidths and transformation parameters simultaneously. It is demonstrated that the correlation between the two dimensions of claim costs is better captured through the bivariate density estimator based on transformed data. Chapter three and four both consider the modelling of Income Protection Insurance (IPI) data, but with different focuses. Chapter three investigates a series of conditional mixture models for modelling claim durations using survival analysis, and examines the consequence of ignoring the important left truncation characteristic of IPI data by fitting the unconditional distributions. It also quantifies the extent of the bias in the resulting parameter estimates when ignoring the left truncation in the data. Furthermore, the best fitted model is extended by introducing a number of covariates into the conditional part of the model. Chapter four explores how to apply various data mining models to better understand Australian IPI. The prediction power of all the data mining methods under consideration is clearly evident. It is also suggested that the principal component analysis is useful to interpret the rating factors employed by the data mining models which drive claim durations of insured lives. At the end, discussions and comparisons are provided on how to weight available predicting variables using different variable combining techniques