1154-Xiang Luan

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

Credibility theory is applied in property and casualty insurance to perform prospective experience rating, i.e., to determine the future premiums to charge based on both past experience and the underlying group rate. Insurance companies assign a credibility factor Z to a specific policyholder’s own past data, and put 1−Z onto the prior mean which is the group rate determined by actuaries to reflect the expected value for all risk classes. This partial credibility takes advantage of both policyholder’s own experience and the entire group’s characteristics, and thus increase the accuracy of estimated value so that the insurance companies can stay competitive 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 three existing mortality models, and produce the non-parametric Buhlmann estimates of the forecasted mortality rates. Numerical results show that the accuracy of forecasted mortality rates are significantly improved after applying the non-parametric Buhlmann method to the Lee-Carter model, the CBD model, and the linear regression-random walk (LR-RW) model. A measure of mean absolute percentage error (MAPE) is adopted to compare the performances in terms of accuracy of mortality
prediction.

Keywords: Credibility Theory; Non-Parametric B¨uhlmann Estimate; Lee-Carter Model; CBD Model; Linear Regression Model; Mortality Rates; MAPE