Deep Learning Incorporated Bühlmann Credibility in the Modified Lee–Carter Mortality Model

Abstract

This research study proposes the inclusion of randomness or an error term in the modified Lee–Carter model, which improves the traditional Lee–Carter model for modeling and forecasting mortality risk for years in the actuarial science field. While the modified Lee–Carter model points out some of its common shortcomings , it has no distributional assumption that has been placed on the error/disturbance term. Incorporating a Gaussian distributional assumption on the error term is proposed, and then, the deep learning technique is used to obtain the parameter estimates. It is a departure from the traditional singular value decomposition estimation technique for estimating the parameters in the model. Finally, the Bühlmann credibility approach is incorporated into the model to determine its forecasting precision compared to the classical Lee–Carter model before applied in actuarial valuations.

Labor Force Participation Rate and Expected Length of Retirement 1989-2066: Comparison of Several OECD Countries

“…Several research suggested tweaks to the Lee-Carter model that would make it more effective at modeling and forecasting rates. Some examples of these adjustments are using a Bayesian method [26] incorporating randomness or an error term into the model [26,27], or employing a state-space model to get around the biodemographic constraint. Moreover, Lee-Carter model has been contrasted with other models, including the neural networks ( [28]), autoregressive integrated moving average (ARIMA) model ( [29]), and modified Lee-Carter model with bias-corrected estimators ( [30]).…”

“…CBD model with a cohort effect was found to provide the greatest fit for males in England and Wales ( [31]), whereas the quadratic CBD model showed the best fit to mortality data in other studies ( [32]). However, other research indicated that variants of Lee-Carter model better suit their data ( [27,33]). Generally, selecting a model requires looking at multiple options, and deciding which one works best with the facts at hand.…”