Incorporating the Bühlmann credibility into mortality models to improve forecasting performances

Abstract

In this paper, we incorporate the Bühlmann credibility into three mortality models (the Lee–Carter model, the Cairns–Blake–Dowd model, and a linear relational model) to improve their forecasting performances, as measured by the MAPE (mean absolute percentage error), using mortality data for the UK. The results show that the MAPE reduction ratios for the three mortality models with the Bühlmann credibility are all significant. More importantly, the MAPEs under the three mortality models with the Bühlmann credibility are very close to each other for each age and forecast year. Thus, by incorporating the Bühlmann credibility we are able to converge the forecasting MAPEs resulting from the three different mortality models to a lower and more consistent level. Moreover, we provide a credibility interpretation with an individual time trend for age x and a group time trend for all ages. Finally, we apply the forecasted mortality rates both with and without the Bühlmann credibility to the net single premiums of life insurance products, and compare the corresponding MAPEs.