Applying P-splines for mortality rates in the Czech Republic

Abstract

Many important classes of liability in life insurance business are sensitive to the direction of future mortality trends. Therefore the prediction of future mortality rates is an issue of fundamental importance for insurance companies. The Lee-Carter model became one of the most applied models and it is used in different countries around the world to forecast age-specific death rates. The main goal of this paper is to apply the method of P-splines to the smoothing and forecasting of two-dimensional mortality tables for the population in the Czech Republic. We use data on males deaths and exposures for the Czech Republic from the Human Mortality Database. We write the code associated with model in R. Many models of mortality can be fitted simply and flexibly with standard statistical software. However, for actuaries the fitting of a model is usually only the first step and the main purpose is the forecasting of mortality. Forecasting is part of the R-package as well. Probability statements derived from the use of a single model and parameter set should be treated with caution. Particularly, we show that the forecasting of the future mortality of the very old (over 80) is less accurate since data can be poor at such ages. Hence, there is a need for awareness of model risk when assessing longevity-related liabilities.