Actuarial Learning for Pension Fund Mortality Forecasting

TL;DR

This study addresses mortality forecasting for pension fund liabilities in Brazil, where subpopulation mortality can diverge from national rates. It adopts actuarial learning, applying ML/AI methods (including decision-tree ensembles and neural networks such as FNN, LSTM, and MHA) alongside the Lee-Carter baseline to predict one-year-ahead mortality rates across age, sex, and calendar year. Results show CatBoost and Lee-Carter achieve similar MAE, while FNN attains the best RMSE, with LSTM/MHA variants offering competitive performance; FNN also yields smoother mortality curves. The work demonstrates practical applications to life expectancy projections, pandemic impact assessment, and cash-flow forecasting for ALM, underscoring the potential for ML-based actuarial methods to enhance pension fund risk management in heterogeneous populations.

Abstract

For the assessment of the financial soundness of a pension fund, it is necessary to take into account mortality forecasting so that longevity risk is consistently incorporated into future cash flows. In this article, we employ machine learning models applied to actuarial science ({\it actuarial learning}) to make mortality predictions for a relevant sample of pension funds' participants. Actuarial learning represents an emerging field that involves the application of machine learning (ML) and artificial intelligence (AI) techniques in actuarial science. This encompasses the use of algorithms and computational models to analyze large sets of actuarial data, such as regression trees, random forest, boosting, XGBoost, CatBoost, and neural networks (eg. FNN, LSTM, and MHA). Our results indicate that some ML/AI algorithms present competitive out-of-sample performance when compared to the classical Lee-Carter model. This may indicate interesting alternatives for consistent liability evaluation and effective pension fund risk management.

Figures (12)

• Figure 1: Top row: time series of (i) exposure and (ii) number of deaths per year for the pension fund. Data from 2012 to 2021, both genders and all ages. Second row: Pyramids of (i) exposure and (ii) number of deaths by age and gender in 2021. Bottom row: Raw log of age-specific mortality rates for males and females for years 2012-2021.
• Figure 2: Architectures of the networks (i) FNN and (ii) FNN and LSTM/MHA jointly used for learning mortality rates.
• Figure 3: Illustration of how the mortality rate series ($m^i_{x,t}$) is handled in LSTM-2 and MHA-2 models. The black line denotes the observed mortality rates arranged by Year and Age, between 2012 and 2018, from 30 to 95 years, for Males. The blue dashed line denotes the observed rates for 2019, from 30 to 95 years, for Males.
• Figure 4: Schematic representation of the temporal cross-validation procedure. In the first step, the training set, represented by the black nodes, consists of data from 2013 to 2015, and mortality predictions are obtained for 2016, represented by the gray nodes, with performance metrics calculated for this year's data. In subsequent steps, data from the next year is added to the training set, and predictions and metrics are obtained for the subsequent year. This procedure is called time series cross-validation.
• Figure 5: Lee-Carter Model. Observed mortality rates in 2019 (dots) with the respective predicted mortality curve. On the left: Males. On the right: Females.