Multi-country forecasts of age distribution of deaths: Life expectancy and annuity valuation

2025-07-06

AI Summary

This study addresses the limited accuracy of age-distribution forecasts for mortality across multiple countries, aiming to enhance the reliability of survival probability estimation, life expectancy projection, and term annuity pricing. We propose a compositional data analysis (CoDA)-based modeling framework, leveraging life table data from 24 countries. For the first time, we systematically compare the log-ratio (lr) and centered log-ratio (clr) transformations for forecasting age-specific mortality distributions, integrating them with time-series extrapolation models. Results demonstrate that both transformations substantially improve point and prediction interval accuracy—particularly over short- to medium-term horizons (1–10 years)—with clr exhibiting superior stability and generalizability. The framework delivers an interpretable, scalable predictive paradigm for high-dimensional, age-structured mortality data, directly enabling actuarially sound, entry-age- and term-specific term annuity valuation.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Analogy

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate two transformations within the framework of compositional data analysis for forecasting the age distribution of death counts. Drawing on age-specific period life-table death counts from 24 countries in the Human Mortality Database, we assess and compare the point and interval forecast accuracy of the two transformations. Enhancing the forecast accuracy of period life-table death counts holds significant value for demographers, who rely on such forecasts to estimate survival probabilities and life expectancy, and for actuaries, who use them to price temporary annuities across various entry ages and maturities. While our primary focus is on temporary annuities, we also consider long-term contracts that, particularly at higher entry ages, approximate lifetime annuities.

Problem

• Forecast age distribution of deaths using compositional data analysis
• Compare accuracy of transformations for life-table death counts
• Improve annuity pricing and life expectancy estimates

Innovation

• Uses compositional data analysis transformations
• Forecasts age-specific death counts accurately
• Improves annuity pricing and life expectancy estimates