Doctor of Philosophy
Statistics and Actuarial Sciences
Bruce L. Jones
Multi-state models are widely used in actuarial science because that they provide a convenient way of representing changes in people's statuses. Calculations are easy if one assumes that the model is a Markov chain. However, the memoryless property of a Markov chain is rarely appropriate.
This thesis considers several mixtures of Markov chains to capture the heterogeneity of people's mortality rates, morbidity rates, recovery rates, and ageing speeds. This heterogeneity may be the result of unobservable factors that affect individuals' health. The focus of this thesis is on investigating the behaviours of intensities of the observable transitions in the mixture models and assessing the applicability of the models.
We first investigate the disability process. Using a mixture model allows the future of the process to be dependent on by its history. We use mixtures of Markov chains with appropriate assumptions to investigate how the intensities of these processes depend on their histories.
We next explore an approach of using mixtures of Markov chains to model the dependence of two lifetimes. The mixture models allow the history of survivorship to affect future survival probabilities, which indicates a non-Markov behaviour. We discuss a simple mixture of two four-state Markov chains and a generalized mixture model.
Finally, we model the physiological ageing process by using mixtures. The traditional physiological ageing process assumes a homogeneous ageing speed. In fact, the ageing speed of each individual is characterized by his/her own health status. Using mixture models allows the process to reflect health status differences.
Zhang, Yuzhou, "Actuarial Modelling with Mixtures of Markov Chains" (2016). Electronic Thesis and Dissertation Repository. 4026.