Longevity risks: modelling and financial engineering

In this dissertation, we investigate various aspects of the systematic mortality risks, in particular, the longevity risks. To describe the precise meaning of random survival probability, we model the systematic mortality risks by generalizing the idea of conditional independence into a dynamical setting. The effects of systematic mortality risks on actuarial science are also analyzed. To evaluate and hedge the longevity riskson capital markets, we build up an arbitrage-free financial market model including survivor bonds. Within an arbitrage-free financial market containing default-free zerocoupon bonds and equities, we study the risk-neutral valuation and hedging strategies for the contingent claims involving longevity risks. The classical Thiele’s differential equation is also generalized under our framework. Furthermore, we study the risk management of longevity risks. Two types of pure longevity derivatives are defined and evaluated with respect to various filtrations. We apply our results on some examples such as longevity securitization and the guaranteed annuity options. We also compare our results to those obtained so far in the literatures.