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Abstract
The thesis develops a coherent framework to calculate the capital required for longevity risk inherent in lifetime annuities. The framework is coherent in that it takes a holistic view of longevity risk and relevant business issues for annuity providers. In contrast to the single factor approach in the contemporary regulatory requirements adopted in Solvency II and Life and General Insurance Capital (LAGIC), capital is quantified in a scientific approach to ensure solvency and capital adequacy to protect the interest of both policyholders and shareholders. Such a framework is necessary to provide for the uncertainty of mortality movements. Continual improvement in mortality and its changing pattern in the past decades have exposed annuity providers to greater longevity risk than ever before. As more retirement income products are developed for aging populations around the world, the need for a coherent capital framework for longevity risk becomes more important.
The approach to capital needs in this thesis is a risk-based alternative to the current method regulatory prescribed method. It starts with best estimate assumption setting and builds on a foundation of Bayesian credibility theory. Both systematic risk from national population mortality development and the idiosyncratic risk intrinsic to the company’s portfolio are captured. The systematic risk capital provides for risks from both random fluctuation around the best estimate assumption and mis-estimation of the best estimates themselves, using stochastic mortality modelling. It also takes into account practical issues such as the ability to raise further capital to allow for an appropriate time horizon. Since a portfolio constitutes a selection of the population, the systematic risk is aggregated with an allowance based on portfolio size and composition to derive the company’s overall capital for longevity risk.
Results show that the current regulatory requirement may understate the capital required, particularly at younger ages. We illustrate that consistency is required for the valuation of best estimate liabilities and capital buffers, as the coherent framework is developed to address the total level of reserves. Model risk is significant, as the results are impacted by model selection. Actuaries should manage this risk and regulators should avoid arbitrage between models, so that capital requirement is calibrated against specific risks underlying the business.