Affine Processes in Life Insurance Mathematics - With a View Towards Solvency II

Abstract

Affine processes have been of great interest in financial mathematics, and with the introduction of Solvency II in life insurance, the need for stochastic modeling of the valuation basis has led to the entry of affine processes into the literature on life insurance mathematics. The thesis begins with a qualitative discussion of Solvency II and the implications for life insurance liabilities. The thesis then considers multidimensional time-inhomogeneous continuous affine processes which are subsequently applied in the valuation of life insurance liabilities, providing a foundation for stochastic modelling of the valuation basis. This leads to the introduction of generalised forward rates, and a theorem is proven that allows for the use of dependent interest and transition rates in e.g. a survival model or a model including the surrender option. Using the theory of affine processes it is also shown how one can model the mortality rate using a CIR process, such that the distribution of the forward rate can be found, allowing for simple simulation of the Solvency II capital requirement. It is shown that the distributional result also holds for certain time-inhomogeneous CIR processes. Thesis for the Master degree in Insurance Mathematics. Department of Mathematical Sciences, University of Copenhagen