Poisson Incorporated Credibility Regression Modelling of Systematic Mortality Risk for Populations with Finite Data

Abstract

This study considered the modeling of systematic mortality risk for populations with finite data using the Poisson incorporated Credibility regression model. For novelty, we have included the credibility regression approach to modelling mortality by assuming the number of annual deaths follow a Poisson distribution. Our model shows improvement in precision levels when estimating mortality risk compared to classical models used in European countries. We have illustrated that our model works optimally when using Kenyan mortality data, comparing male and female lives under the different strategies, thus making better predictions than the classical Lee–Carter (LC) and Cairns–Blake–Dowd (CBD) models. The mean absolute forecast error (MAFE), mean absolute percentage forecast error (MAPFE), root mean square error (RMSE), and root mean square forecast error (RMSFE) under the incorporated credibility regression model are much lower than the values obtained without incorporation of the Buhlmann credibility approach. The findings of this research will help insurance companies, pension firms, and government agencies in sub-Saharan countries model and forecast systematic mortality risks accurately. Finally, the results are essential in actuarial modelling and pricing, thus making life assurance products affordable for most people in low-income African countries.