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(2022) Wheadon, DanielThesisThis thesis explores the effectiveness of some government policies regarding retirement incomes, namely the Australian old age pension and mandatory retirement saving through superannuation. Using an overlapping generations model for a small open economy, I investigate the effect of introducing an adjustable (non-linear) taper rate to a means-tested public age pension. Unlike a linear taper rate, a non-linear taper rate can be adjusted without affecting eligibility for the pension. Both a progressive taper rate (that increases with income) and a regressive taper rate are considered. A strongly regressive non-linear test with a low average taper rate is marginally preferable to the best-performing linear test. Means testing the pension tends to favour higher income earners but introducing a non-linear test can reduce the welfare cost to lower and middle-income earners. The thesis then considers pension policies in the context of a population with Gul-Pesendorfer style self-control preferences, in which households experience temptation to over-consume in the near term and must exercise costly self-control to save for retirement. First, I consider the role of means testing a public pension and find that the benefits of the means test are smaller when self-control preferences are stronger as the expected cost savings are smaller than they would otherwise be, and the population increasingly values the pension as a commitment device. I also find that populations with higher self-control costs prefer lower taper rates on the pension means test, and a universal pension may be preferred if self-control costs are sufficiently high. Second, two- and three-period life-cycle models are used to examine the effectiveness of a policy maker directly mandating that households save for retirement. I find that increasing the contribution rate on a savings mandate always leads to a utility gain for households with self-control preferences provided voluntary household savings are not crowded out. For households without self-control preferences there are no utility losses provided voluntary savings are not crowded out. A savings mandate will not necessarily increase household savings unless voluntary savings are fully crowded out. The optimal choice of contribution rate was found to largely depend upon the agent’s discount factor rather than the intensity of the self-control preferences.
(2023) Vhudzijena, MichelleThesisMortality 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.