Abstract
This manuscript proposes an approach for large-scale mortality modelling and forecasting with the assumption of locally-coherence of the mortality forecasts. In general, the coherence prevents diverging long-term mortality forecasts between two or more populations. Despite being considered a desirable property in a multi-population modelling framework, it could be perceived as a strong assumption when a large collection of countries is considered. We propose a neural network model which requires the coherence of the mortality forecasts only within sub-groups of similar populations. The architecture is designed to be easily interpretable and induces the creation of some clusters of countries with similar mortality patterns. This aspect also makes the model an interesting tool for analysing similarities and differences between different countries’ mortality dynamics and identifying opportunities for longevity risk diversification and mitigation. An extensive set of numerical experiments performed using all the available data from the Human Mortality Database shows that our model produces more accurate mortality forecasts with respect to some well-known stochastic mortality models. Furthermore, a massive reduction of the parameters to optimise is achieved with respect to the benchmark mortality models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atance, D., Balbás, A., Navarro, E.: Constructing dynamic life tables with a single-factor model. Decis. Econ. Finan. 43(2), 787–825 (2020)
Bengio, Y., Ducharme, R., Vincent, P., Jauvin, C.: A neural probabilistic language model. J. Mach. Learn. Res. 3, 1137–1155 (2003)
Boonen, T.J., Li, H.: Modeling and forecasting mortality with economic growth: a multipopulation approach. Demography 54(5), 1921–1946 (2017)
Booth, H., Tickle, L.: Mortality modelling and forecasting: a review of methods. Ann. Actuarial Sci. 3(1–2), 3–43 (2008)
Bozzo, G., Levantesi, S., Menzietti, M.: Longevity risk and economic growth in sub-populations: evidence from Italy. Decis. Econ. Finan. 44(1), 101–115 (2021)
Brouhns, N., Denuit, M., Vermunt, J.K.: A poisson log-bilinear regression approach to the construction of projected lifetables. Insurance Math. Econom. 31(3), 373–393 (2002)
Cairns, A.J., Blake, D., Dowd, K.: A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J. Risk Insurance 73(4), 687–718 (2006)
Dong, Y., Huang, F., Yu, H., Haberman, S.: Multi-population mortality forecasting using tensor decomposition. Scand. Actuar. J. 2020(8), 754–775 (2020)
Enchev, V., Kleinow, T., Cairns, A.J.: Multi-population mortality models: fitting, forecasting and comparisons. Scand. Actuar. J. 2017(4), 319–342 (2017)
Giordano, G., Haberman, S., Russolillo, M.: Coherent modeling of mortality patterns for age-specific subgroups. Decis. Econ. Finan. 42(1), 189–204 (2019)
Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT press, (2016)
Guibert, Q., Loisel, S., Lopez, O., Piette, P.: Bridging the li-carter’s gap: a locally coherent mortality forecast approach (2020)
Guo, C., Berkhahn, F.: Entity embeddings of categorical variables. Preprint arXiv:1604.06737 (2016)
Hainaut, D.: A neural-network analyzer for mortality forecast. ASTIN Bull. J. IAA 48(2), 481–508 (2018)
Hitaj, A., Mercuri, L., Rroji, E.: Lévy carma models for shocks in mortality. Decis. Econ. Finan. 42(1), 205–227 (2019)
Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2(5), 359–366 (1989)
Hyndman, R.J., Booth, H., Yasmeen, F.: Coherent mortality forecasting: the product-ratio method with functional time series models. Demography 50(1), 261–283 (2013)
Kleinow, T.: A common age effect model for the mortality of multiple populations. Insurance Math. Econom. 63, 147–152 (2015)
Lee, R.D., Carter, L.R.: Modeling and forecasting us mortality. J. Am. Stat. Assoc. 87(419), 659–671 (1992)
Levantesi, S., Nigri, A., Piscopo, G.: Clustering-based simultaneous forecasting of life expectancy time series through long-short term memory neural networks. Int. J. Approx. Reason. 140, 282–297 (2022)
Li, N., Lee, R.: Coherent mortality forecasts for a group of populations: an extension of the lee-carter method. Demography 42(3), 575–594 (2005)
Lindholm, M., Palmborg, L.: Efficient use of data for lstm mortality forecasting. Eur. Actuar. J. 1–30 (2022)
Marino, M., Levantesi, S., Nigri, A.: A neural approach to improve the lee-carter mortality density forecasts. North Am. Actuar. J. 1–18 (2022)
Nigri, A., Levantesi, S., Marino, M., Scognamiglio, S., Perla, F.: A deep learning integrated lee-carter model. Risks 7(1), 33 (2019)
Perla, F., Richman, R., Scognamiglio, S., Wüthrich, M.V.: Time-series forecasting of mortality rates using deep learning. Scand. Actuar. J. 1–27 (2021)
Renshaw, A.E., Haberman, S.: Lee-carter mortality forecasting with age-specific enhancement. Insurance Math. Econom. 33(2), 255–272 (2003)
Renshaw, A.E., Haberman, S.: A cohort-based extension to the lee-carter model for mortality reduction factors. Insurance Math. Econom. 38(3), 556–570 (2006)
Richman, R.: Ai in actuarial science-a review of recent advances-part 1. Ann. Actuar. Sci. 15(2), 207–229 (2021)
Richman, R.: Ai in actuarial science-a review of recent advances-part 2. Ann. Actuar. Sci. 15(2), 230–258 (2021)
Richman, R., Wüthrich, M.V.: A neural network extension of the lee-carter model to multiple populations. Ann. Actuar. Sci. 15(2), 346–366 (2021)
Russolillo, M., Giordano, G., Haberman, S.: Extending the lee-carter model: a three-way decomposition. Scand. Actuar. J. 2011(2), 96–117 (2011)
Schnürch, S., Korn, R.: Point and interval forecasts of death rates using neural networks. ASTIN Bull. J. IAA 52(1), 333–360 (2022)
Schnürch, S., Kleinow, T., Korn, R.: Clustering-based extensions of the common age effect multi-population mortality model. Risks 9(3), 45 (2021)
Scognamiglio, S.: A multi-population locally-coherent mortality model. In: Mathematical and Statistical Methods for Actuarial Science and Finance, pp. 423–428 (2022). Springer
Scognamiglio, S.: Calibrating the lee-carter and the poisson lee-carter models via neural networks. ASTIN Bull. J. IAA 1–43 (2022)
Shang, H.L., Haberman, S.: Forecasting multiple functional time series in a group structure: an application to mortality. ASTIN Bull. J. IAA 50(2), 357–379 (2020)
Wilmoth, J.R., Shkolnikov, V.: Human mortality database. University of California, Berkeley (US), and Max Planck Institute for Demographic Research (Germany) (2021)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Perla, F., Scognamiglio, S. Locally-coherent multi-population mortality modelling via neural networks. Decisions Econ Finan 46, 157–176 (2023). https://doi.org/10.1007/s10203-022-00382-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10203-022-00382-x
Keywords
- Multi-population mortality modelling
- Neural networks
- Coherence mortality forecasting
- Human mortality database