In this paper, we take the point of view of an insurer dealing with life annuities, which aims at building up a (partial) internal model in order to quantify the impact of mortality risks, namely process and longevity risk, in view of taking appropriate risk management actions. The model we propose focuses on the annual number of deaths in a given cohort, which we represent allowing for a random mortality rate. The model is then implemented for capital allocation purposes. We investigate the amount of the required capital for a given life annuity portfolio, based on solvency targets which could be adopted within internal models.
