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Abstract
This thesis develops new models and methodologies for the modelling and management of longevity risk. A rich set of mathematical tools have been developed for interest rate and credit risk modelling, and these tools have led to numerous financial innovations. As a result, securities are actively traded in interest rate and credit risk markets. In contrast, a market for longevity risk has been slow to develop, and typical mortality models used by actuaries do not fit into common financial pricing frameworks. To address this gap, this thesis provides a mathematical framework for the modelling, pricing, and management of longevity risk.
A multi-factor mortality model and estimation procedure for historical mortality data within an affine term structure modelling framework is proposed and developed. We construct the affine model to generate consistent survivor curve forecasts for all cohorts. A detailed analysis of the fit of the results and out-of-sample performance is conducted. We show that the framework meets a number of mortality modelling criteria: it is parsimonious, factors are easily interpreted, it is transparent, forecasting is easily implemented, sample paths are easily generated and we may specify a non-trivial correlation structure between factors.
The modelling framework is extended to include a pricing measure that allows us to apply a longevity risk premium to cohort survivor curves. This generalises Wang transform and Sharpe Ratio pricing methods. We then price longevity-linked securities and derivatives in an arbitrage-free framework; this allows cohorts to be represented by a forward mortality model, which is ideally suited to analysing the risk management strategies of an insurer writing annuity products to multiple cohorts.
Finally the thesis develops analytic tools for pricing deferred guaranteed annuity and pure endowment options that may be embedded in complex insurance products. We present a time-inhomogeneous affine mortality model, and use Laplace transform techniques to derive a joint interest and mortality probability density function. The option prices can then be solved under the risk-neutral measure using numerical integration techniques. This provides a fast and efficient option pricing technique, without using approximation methods.