Forecasting sub-population mortality using credibility theory

2025-07-16

AI Summary

To address unreliable mortality forecasting for small subpopulations, this paper proposes a credibility-theory-based hybrid forecasting framework. Methodologically, we extend classical credibility theory to latent stochastic process-driven mortality models—without requiring specification of the underlying superpopulation model—and integrate Lee-Carter-type structure to construct a weighted average predictor, where superpopulation forecasts serve as benchmarks and subpopulation-specific features provide calibration signals; we further derive an explicit analytical expression for the prediction mean squared error. Our key contribution is the first systematic integration of credibility theory with latent-variable mortality models, yielding a model-agnostic, analytically tractable, and robust forecasting paradigm. Simulation studies demonstrate that the method achieves a significant trade-off between superpopulation forecast accuracy and subpopulation adaptability, effectively mitigating small-sample bias.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Graphical ModelsCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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 mean squared error of prediction. 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.

Problem

• Forecast mortality rates for small sub-populations using credibility theory
• Combine super-population and sub-population mortality rate predictions
• Derive explicit mean squared error for the proposed predictor

Innovation

• Extends credibility theory for latent mortality processes
• Uses weighted averages for sub-population mortality forecasts
• Derives explicit mean squared error expression