Model mortality rates using property and casualty insurance reserving methods

Abstract

The chain-ladder model is the most widely used technique for property and casualty insurance to estimate unpaid claims, including incurred but not reported (IBNR) claims. Inspired by the reserving method, we first apply a distribution-free method (the chain-ladder model) and its variant and a distributional method (the lognormal model) to project future mortality rates. Next, to simulate mortality rates for more applications, we also propose corresponding stochastic versions associated with both the lognormal model and the variant of the chain-ladder model. Finally, we demonstrate numerical illustrations with mortality data from the Human Mortality Database for both genders of the US, the UK, and Japan. To compare the forecasting performances of the proposed three models and the other five models (the Lee-Carter model, the Renshaw-Haberman model, the Cairns-Blake-Dowd model, the M6 and M7 models), we adopt mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) as metrics. Numerical illustrations show that the proposed three models overall outperform the other five models.