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

TL;DR

This paper develops Gaussian process models to analyze and project pension fund mortality rates, accounting for socioeconomic disparities and data sparsity, with applications to Brazilian pension funds.

Contribution

It introduces a flexible Gaussian process framework for modeling pensioner mortality rates, improving fit and uncertainty quantification over parametric methods.

Findings

GP models outperform parametric approaches in fit and uncertainty estimation

Models effectively capture mortality deflators relative to reference populations

Application to Brazilian pension funds demonstrates practical utility

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.