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  • Modelling mortality heterogeneity using health trajectories and multimorbidity
    (2023) Vhudzijena, Michelle
    Thesis
    Mortality heterogeneity is a generally well understood area of longevity risk that remains relatively unexplored in the actuarial pricing of longevity linked products. However, with increasing amounts of longitudinal individual level data, there exists an extraordinary opportunity to derive more nuanced and realistic mortality risk profiles that can improve the design and demand of annuities and other longevity linked products. Deriving mortality risk profiles using the clustering of health trajectories and unsupervised machine learning algorithms is seldomly investigated in the literature. The first project in this thesis applies a three dimensional k–means clustering algorithm to joint trajectories of self reported health and body mass index to develop mortality risk profiles. We are able to determine distinct mortality risk profiles from the clusters that exhibit significant differences in life expectancy and annuity prices for both males and females at varying ages. Disregarding health status in longevity linked products has been shown to cause adverse selection from individuals with chronic conditions due to inaccurate pricing of mortality and morbidity risks. However, we are unaware of work in the actuarial literature that shows the impact of risk factors on health status. Therefore, the second project explores the effectiveness of utilising hidden markov models with covariates to demonstrate mortality heterogeneity. We find that the clusters generated by the hidden Markov models have a better fit to empirical data than models without clustering. It is important to address the link between multimorbidity and the pricing of health and longevity linked products in the actuarial literature. The last project in this thesis seeks to find the best way to incorporate multimorbidity in the pricing of long term care products. We compare two different ways of incorporating multimorbidity in multiple state models. We find that our proposed five state multimorbidity and functional disability model is able to capture the dynamics of health over time more accurately than the three state health and functional disability model with a multimorbidity predictor. The results from the later model weakly suggest morbidity expansion when in effect there is very strong evidence of morbidity expansion. This inadvertently leads to the gross mispricing of life annuities, long term care and life care annuities.