First-Order Mortality Basis for Life Annuities

Mortality improvements pose a challenge for the life annuity business. For the management of such portfolios, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp, where the dynamics of the time index is described by a random walk with drift. Starting from such a best estimate of future mortality (called second-order mortality basis in actuarial science), the paper explains how to determine a conservative life table serving as first-order mortality basis. The idea is to replace the stochastic projected life table with a deterministic conservative one, and to assume mutual independence for the remaining life times. The paper then studies the distribution of the present value of the payments made to a closed group of annuitants. It turns out that De Pril–Panjer algorithm can be used for that purpose under first-order mortality basis. The connection with ruin probabilities is briefly discussed. An inequality between the distribution of the present value of future annuity payments under first-order and second-order mortality basis is provided, which allows to link value-at-risk computed under these two sets of assumptions. A numerical example performed on Belgian mortality statistics illustrates how the approach proposed in this paper can be implemented in practice.