A Pseudo Non-Parametric Buhlmann Credibility Approach to Modeling Mortality Rates

Credibility theory is applied in property and casualty insurance to perform prospective experiencerating, i.e., to determine the future premiums to charge based on both past experienceand the underlying group rate. Insurance companies assign a credibility factor Z to a specificpolicyholder’s own past data, and put 1 − Z onto the prior mean which is the group rate determinedby actuaries to reflect the expected value for all risk classes. This partial credibilitytakes advantage of both policyholder’s own experience and the entire group’s characteristics,and thus increases the accuracy of estimated value so that the insurance companies can staycompetitive in the market. Faced with its popular applications in property and casualty insurance,this project aims to apply the credibility theory to projected mortality rates from threeexisting mortality models. The approach presented in this project violates one of the conditions,and thus produces the pseudo non-parametric Bühlmann estimates of the forecasted mortalityrates. Numerical results show that the accuracy of forecasted mortality rates are significantlyimproved after applying the non-parametric Bühlmann method to the Lee-Carter model, theCBD model, and the linear regression-random walk (LR-RW) model. A measure of mean absolutepercentage error (MAPE) is adopted to compare the performances in terms of accuracy ofmortality prediction.