Mortality modelling and forecasting using generalised age-period-cohort models and neural networks
Article Sidebar
Main Article Content
Abstract
Modelling and forecasting mortality risk are key tasks in demography as well as for social security institutions and insurance companies. Traditionally used stochastic mortality models such as the Lee-Carter model, require meeting assumptions which cannot always be met in real-life scenarios. These include, for example, the condition of time independence of age- specific improvement rates. An alternative approach to mortality modelling is based on deep neural networks. Previous works in the field primarily focus on recurrent neural networks, typically used in time series forecasting problems. This work aims to compare and analyse the effectiveness of both types of methods in mortality modelling and forecasting based on nine European populations. The study uses data from the Human Mortality Database.
Additionally, we propose a hyperparameter tuning framework for the feedforward neural network model used in the study.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D. G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y. Zhang, X. (2016).
TensorFlow: a system for large-scale machine learning, Proceedings of the 12th U SENIX Symposium on Operating Systems Design and Implementation (OSDI ’16), 265–283.
Antonio, K., Bardoutsos, A., Ouburg, W. (2015). Bayesian Poisson log-bilinear mod- els for mortality projections with multiple populations, European Actuarial Journal, 5 (2), 245–281.
Ashofteh A., Bravo, J. M. (2021). Life Table Forecasting in COVID-19 Times: An Ensem- ble Learning Approach, 16th Iberian Conference on Information Systems and Technolo- gies (CISTI), Chaves, Portugal, 1–6.
Ayuso, M., Bravo, J. M., Holzmann, R. (2021). Getting life expectancy estimates right for pension policy: period versus cohort approach. Journal of Pension Economics and Finance, 20 (2), 212–231.
Bengio, Y., Ducharme, R., Vincent, P. Jauvin, C. (2003). A neural probabilistic lan- guage model. Journal of Machine Learning Research, 3 (2), 1137–1155.
Breiman, L. (1996). Stacked regressions. Machine learning, 24, 49–64.
Brouhns, N., Denuit M., Vermunt, J. (2002). A Poisson Log-Bilinear regression approach to the construction of projected life tables, Insurance: Mathematics and Eco- nomics, 31 (3), 373–393.
Cairns, A. J., Blake, D., Dowd, K., (2006). A two-factor model for stochastic mortal- ity with parameter uncertainty: theory and calibration, Journal of Risk and Insurance, 73 (4), 687–718.
Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States, North American Actuarial Journal, 3 (1), 1–35.
Carracedo, P., Debón, A., Iftimi, A., Montes, F. (2018). Detecting spatio-temporal mor- tality clusters of European countries by sex and age. International journal for equity in health, 17, 1–19.
Chen, H., MacMinn, R., Sun, T., (2015). Multi-population mortality models: a factor copula approach, Insurance: Mathematics and Economics, 63, 135–146.
Chollet, F. (2015). Keras: the Python deep learning library.
Deprez, P., Shevchenko, P., Wüthrich, M. (2017). Machine learning techniques for mortality modeling, European Actuarial Journal, 7 (2), 337–352.
Fisher, R. A. (1922). On the Mathematical Foundations of Theoretical Statistics”, Phil- osophical Transactions of the Royal Society of London. Series A (222), 309–368.
Gaille, S., Sherris, M. (2011). Modelling mortality with common stochastic long-run trends. The Geneva Papers on Risk and Insurance-Issues and Practice, 36, 595–621.
Hainaut, D. (2018). A neural-network analyzer for mortality forecast, Astin Bulletin, 48 (2), 481–508.
Hinton, G., Srivastava, N., Krizhevsky, A., Sutskever, I. Salakhutdinov, R. (2012).
Improving neural networks by preventing co-adaptation of feature detectors. arXiv, arXiv:1207.0580.
Ioffe, S. Szegedy, C. (2015). Batch normalization: accelerating deep network training by reducing internal covariate shift. Proceedings of the 32nd International Conference on Machine Learning, PMLR 37, 448–456.
Kessy, S. R., Sherris, M., Villegas, A. M., Ziveyi, J. (2022). Mortality forecasting using stacked regression ensembles, Scandinavian Actuarial Journal, 2022 (7), 591–626.
Lee, R. D., Carter L. R. (1992). Modeling and Forecasting U. S. Mortality, Journal of the American Statistical Association, 87 (419), 659–671.
Levantesi, S., Pizzorusso, V. (2019). Application of Machine Learning to Mortality Modeling and Forecasting, Risks, 7 (1), 26.
Li, J. S.-H., Chan, W.-S., Zhou, R. (2017). Semicoherent multipopulation mortality modeling: the impact on longevity risk securitization, Journal of Risk and Insurance, 84 (3), 1025–1065.
Li, N., Lee, R. D. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42 (3), 575–594.
Nair, V. Hinton, G. (2010). Rectified linear units improve restricted Boltzmann machines. In: Proceedings of the 27th International Conference on Machine Learning, 807–814.
Nigri, A., Levantesi, S., Marino, M., Scognamiglio, S., Perla, F. (2019). A Deep Learn- ing Integrated Lee–Carter Model, Risks, 7 (33), 1–16. [26] OECD (2023), Pensions at a Glance 2023: OECD and G20 Indicators, OECD Publish- ing, 214.
Özen, S., Şahin, Ş. (2021). A two-population mortality model to assess longevity basis risk, Risks, 9 (2), 44.
Perez-Panades, J., Botella-Rocamora, P., Martinez-Beneito, M. A. (2020). Beyond stan- dardized mortality ratios; some uses of smoothed age-specific mortality rates on small areas studies. International Journal of Health Geographics, 19, 1–14.
Perla, F., Richman, R., Scognamiglio, S., Wüthrich, M. (2021). Time-series forecast- ing of mortality rates using deep learning, Scandinavian Actuarial Journal, 2021 (7), 572–598.
Perla, F., Scognamiglio, S. (2022), Locally-coherent multi-population mortality mod- elling via neural networks, Decisions in Economics and Finance, 46 (1), 157–176.
Perla, F., Richman, R., Scognamiglio, S., Wüthrich, M. V. (2024). Accurate and explain- able mortality forecasting with the LocalGLMnet. Scandinavian Actuarial Journal, 2024 (7), 739–761.
Plat, R. (2009). On Stochastic Mortality Modeling, Insurance: Mathematics and Eco- nomics, 45 (3), 393–404.
Renshaw A. E., Haberman S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38 (3), 556–570.
Haberman S, Renshaw A. (2011). A Comparative Study of Parametric Mortality Pro- jection Models, Insurance: Mathematics and Economics, 48 (1), 35–55.
Richman, R., Wüthrich, M. (2021). A neural network extension of the Lee–Carter model to multiple populations. Annals of Actuarial Science, 15 (2), 346–366.
Shen, Y., Yang, X., Liu, H., Li, Z. (2024). Advancing mortality rate prediction in Euro- pean population clusters: integrating deep learning and multiscale analysis. Scientific Reports, 14 (1), 6255.
Schnürch, S., Korn, R. (2022). Point and interval forecasts of death rates using neural networks, ASTIN Bulletin: The Journal of the IAA, 52 (1), 333–360.
Scognamiglio, S. (2022). Calibrating the Lee-Carter and the Poisson Lee-Carter mod- els via neural networks, ASTIN Bulletin: The Journal of the IAA, 52 (2), 519–561.
Scognamiglio, S. (2024). Multi-population mortality modelling and forecasting with divergence bounds. Annals of Operations Research, 1–19.
Villegas, A. M., Kaishev, V. K., Millossovich, P. (2018). StMoMo: An R Package for Sto- chastic Mortality Modeling, Journal of Statistical Software, 84 (3), 1–38.
Wang, J., Wen, L., Xiao, L., Wang, C. (2024). Time-series forecasting of mortality rates using transformer, Scandinavian Actuarial Journal, 2024 (2), 109–123.
Wiśniowski A, Smith P. W., Bijak J, Raymer J, Forster JJ. (2015). Bayesian Population Forecasting: Extending the Lee-Carter Method. Demography. 52 (3), 1035–1059.
World Bank Group (2024). Mortality rate, adult, male (per 1,000 male adults) - Euro- pean Union, https://data.worldbank.org/indicator/SP.DYN.AMRT.MA?locations=E
Zhou, R., Li, J. S.-H., Tan, K. S. (2013). Pricing standardized mortality securitizations: a two-population model with transitory jump effects, The Journal of Risk and Insur- ance, 80 (3), 733–774.