Stochastic Mortality Modelling and Management of Longevity Risk with Pricing and Reserving Applications to Annuity Products
Over the past decades, the life insurance sector has been faced with a number of challenges that emerged as a result of the growing longevity and stagnating birth rates for highly developed societies. In the field of actuarial application one could therefore ask for the implications of (long-term) mortality trends and (short-term) population fluctuation on an insurer's pricing and reserving of pension contracts, particularly in interaction with uncertainty in the capital markets. The first part of the thesis focuses on the mathematical description and projection of the mortality of homogeneous populations or insurance cohorts. Besides a survey of the most important representatives, a comprehensive analysis and comparison of stochastic and deterministic mortality forecasting models is carried out. In the second part a full stochastic model approach for two typical old-age provision products is set up and applied in terms of a management of longevity risk. On the one hand, a deferred conventional life annuity is analysed with regard to the combined effects of stochastic mortality and interest rates on different premium principles and risk capital allocation. On the other hand, a modern unit-linked annuity insurance, namely a deferred variable annuity contract, with an additional guaranteed minimum death benefit during the deferment period and a minimum income benefit at retirement is discussed. Mathematically, the guarantees represent options on the greater of the net asset value and a predetermined insurance benefit. For this reason, the existence and uniqueness of an extra fair percentage guarantee charge is proven. Furthermore, a sensitivity analysis of the fair charge and risk neutral option prices concerning different model parameters is considered and several profitability and risk measures are determined.