Actuarial challenges in mortality modelling

The temporal change of the mortality structure forced actuaries to adopt a prospective vision of the mortality. This new perspective generates interesting issues to investigate along life tables. These issues may be classified into two categories: Mid-Table issues and End-Table issues. Mid-Table refers to the portion of the life table from young adults to early old ages (around 95 years old). The abundance of data in this region of ages allows to clearly detect trends in mortality rates. Then, one of the challenges for actuaries in this part of life table mostly concern simulations. End-Table refers to the portion of the life table above 95 years old. Contrary to Mid-Table, this region has very few data. As a consequence, mortality trends are hardly detectable which makes End-Table extrapolation an intricate task. Estimated mortality in this region is then not so much robust. The purpose of the thesis was to propose solutions to overcome those challenges. The first part of the thesis presents solutions to Mid-Table issues. They are based on the comonotonic approach. Stochastic approximations for the present value of future benefits for a homogeneous portfolio of annuitants in the LC model as well as in the CBD model were built. These stochastic approximations allow to simulate the portfolio extinction with a small number of simulated random variables with a high degree of precision. The second part of the thesis focuses on End-Table issues. The use of Extreme Value Theory which does not require any parametric form of the lifetime distribution, helps us to obtain a satisfying adjustment for mortality at older ages. In addition, it contributes to the debate on the existence of an upper limit for the age.