Credibility Adjustment of the Lee-Carter Longevity Model for Multiple Populations

In this paper we are interested in applying Bühlmann-Straub credibility for a multiple population model, in particular, in presence of small sized populations. We introduce a parsimonious extension of the classic Lee and Carter model in a similar manner as the joint-κ model, which does impose a common factor to the considered populations. Hence, we propose an adjustment procedure based on the Bühlmann-Straub linear credibility into a Lee-Carter model in order to take into account the heterogeneity among the populations while allowing for learning effect for each population. The updating mechanism is based on the credibility estimations of future mortality rates depending on past observations through a recursive credibility formula. By doing so, the forecasts weight the importance of the information stemming from the single population while taking into account the neighboring populations. The proposed methodology is applied to real-world datasets and comparisons to classic mortality models is proposed.