Forecasting sub-population mortality using credibility theory

TL;DR

This paper extends credibility theory to forecast mortality rates for small sub-populations by combining super-population forecasts with sub-population data, especially when sub-population data is limited or unreliable.

Contribution

It introduces a new credibility predictor that integrates super-population and sub-population mortality forecasts, applicable across various super-population models.

Findings

The credibility predictor effectively balances super- and sub-population information.

Explicit formulas for forecast error are derived for the proposed method.

Simulation results demonstrate the predictor's practical utility.

Abstract

The focus of the present paper is to forecast mortality rates for small sub-populations that are parts of a larger super-population. In this setting the assumption is that it is possible to produce reliable forecasts for the super-population, but the sub-populations may be too small or lack sufficient history to produce reliable forecasts if modelled separately. This setup is aligned with the ideas that underpin credibility theory, and in the present paper the classical credibility theory approach is extended to be able to handle the situation where future mortality rates are driven by a latent stochastic process, as is the case for, e.g., Lee-Carter type models. This results in sub-population credibility predictors that are weighted averages of expected future super-population mortality rates and expected future sub-population specific mortality rates. Due to the predictor's simple structure it is possible to derive an explicit expression for the expected quadratic forecast error. Moreover, the proposed credibility modelling approach does not depend on the specific form of the super-population model, making it broadly applicable regardless of the chosen forecasting model for the super-population. The performance of the suggested sub-population credibility predictor is illustrated on simulated population data. These illustrations highlight how the credibility predictor serves as a compromise between only using a super-population model, and only using a potentially unreliable sub-population specific model.