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Abstract
Insurance claims can have very long durations, from the date they are made known to the insurance company to the date the liability is settled. These reported but not yet finalised claims form a considerable part of the insurance liabilities of an insurance company, that is, the monies it need to set aside to pay for claims it is liable for. Traditionally, such analyses are undertaken on an aggregate basis, that is, the ultimate cost of a group of claims are projected in aggregate rather than finding the expected ultimate cost based on analysing and projecting individual claims.
This thesis is concerned with modelling the claims development behaviour of individual long tailed claims. The model developed herein (CDP model) is an individual claims reserving model, since it is concerned with individual claim trajectories and their ultimate costs.
While it may be possible to model the complete claim process in a multivariate framework with appropriate dependence structure, we have chosen to decompose the overall claim process into simpler components with a conditional hierarchical structure. The decomposition allows the complicated claims process to be represented with four simpler processes, turning each claim trajectory into four short time series.
The time series models of Generalised Linear Auto-Regression and Moving Average are used to analyse the component series. The results of these models are discussed; while some of the results conform to our intuition regarding the claim development behaviours, others have been surprising.
We use the CDP framework to project individual ultimate claims costs using simulation methods. We compared the accuracy of the predictions using the CDP model. We also aggregated the individual claims and investigated the usefulness of the method as a new valuation technique that insurance companies can use to project their claims liabilities.
We developed and investigated some important extensions to the basic CDP framework. They include making an allowance for censoring, where not all claims are observed to their finalisation; incorporating random effects, to allow for claimants differing attitudes towards the claims process.