A Geostatistical Approach for Dynamic Life Tables. The effect of mortality on remaining lifetime and annuities

Dynamic life tables arise as an alternative to the standard (static) life ta-ble with the aim of incorporating the evolution of mortality over time. The parametric model introduced by Lee and Carter in 1992 for projected mor-tality rates in the US is one of the most outstanding and has been largely used since then. Different versions of the model have been developed but all of them, together with other parametric models, consider the observed mortality rates as independent observations. This is a difficult hypothesis to hold when looking at the graph of the residuals obtained with any of these methods. Methods of adjustment and prediction based on geostatistical techniques which exploit the dependence structure existing among the residuals are an alternative approach to classical methods. Dynamic life tables can be consid-ered as a two-way table on a grid equally spaced in either the vertical (age) or horizontal (year) direction, and the data can be decomposed into a deter-ministic large-scale variation (trend) plus a stochastic small-scale variation (residuals). Preprint submitted to Insurance: Mathematics and Economics February 8, 2010 Our contribution consists of applying geostatistical techniques for esti-mating the dependence structure of the mortality data and for prediction purposes, also including the influence of the year of birth (cohort). We com-pare the performance of this new approach with different versions of the Lee-Carter model. Additionally, we obtain bootstrap confidence intervals for predicted qxt resulting from applying both methodologies, and we study their influence on the predictions of e65t and a65t