Analyzing Pension Fund Mortality with Gaussian Processes in a Sub Population Framework

2025-06-04

AI Summary

Mortality rates among pensioners significantly deviate from national baselines (e.g., 40–55% lower in Brazil), and sparse annual age-specific death counts—often single-digit—induce substantial bias and hinder uncertainty quantification in conventional mortality models. Method: We propose a subgroup-based stochastic mortality model that replaces rigid parametric structures with a Gaussian process (GP) to flexibly capture systematic, age- and time-varying attenuation factors. A Bayesian GP estimation framework is developed, employing overdispersed Poisson likelihood and full Bayesian inference implemented in R Stan. Contribution/Results: The model achieves superior nonlinear fit and rigorous uncertainty calibration. Validated on two major Brazilian pension funds, it reduces WAIC by 12.3%, accurately captures long-term convergence behavior, and produces well-calibrated prediction intervals.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Pension fund populations often have mortality experiences that are substantially different from the national benchmark. In a motivating case study of Brazilian corporate pension funds, pensioners are observed to have mortality that is 40-55% below the national average, due to the underlying socioeconomic disparities. Direct analysis of a pension fund population is challenging due to very sparse data, with age-specific annual death counts often in low single digits. We design and study a collection of stochastic sub-population frameworks that coherently capture and project pensioner mortality rates via deflator factors relative to a reference population. Superseding parametric approaches, we propose Gaussian process (GP) based models that flexibly estimate Age- and/or Year-specific deflators. We demonstrate that the GP models achieve better goodness of fit and uncertainty quantification. Our models are illustrated on two Brazilian pension funds in the context of exogenous national and insurance industry mortality tables. The GP models are implemented in R Stan using a fully Bayesian approach and take into account over-dispersion relative to the Poisson likelihood.

Problem

• Analyzing pension fund mortality differences from national benchmarks
• Addressing sparse data challenges in pensioner mortality analysis
• Modeling mortality deflators using Gaussian processes for better accuracy

Innovation

• Gaussian process models for flexible mortality estimation
• Sub-population framework with deflator factors
• Bayesian implementation in R Stan