A neural-network analyzer for mortality forecast. (English) Zbl 1390.91186

Summary: This article proposes a neural-network approach to predict and simulate human mortality rates. This semi-parametric model is capable to detect and duplicate non-linearities observed in the evolution of log-forces of mortality. The method proceeds in two steps. During the first stage, a neural-network-based generalization of the principal component analysis summarizes the information carried by the surface of log-mortality rates in a small number of latent factors. In the second step, these latent factors are forecast with an econometric model. The term structure of log-forces of mortality is next reconstructed by an inverse transformation. The neural analyzer is adjusted to French, UK and US mortality rates, over the period 1946–2000 and validated with data from 2001 to 2014. Numerical experiments reveal that the neural approach has an excellent predictive power, compared to the Lee-Carter model with and without cohort effects.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
92D20 Protein sequences, DNA sequences
Full Text: DOI


[1] Abdulkarim, S. A.; Garko, A. B., Forecasting maternal mortality rate using particle Swarm optimization based artificial neural network, Dutse Journal of Pure and Applied Sciences, 1, 55-59, (2015)
[2] Antonio, K.; Bardoutsos, A.; Ouburg, W., Bayesian Poisson log-bilinear models for mortality projections with multiple populations, European Actuarial Journal, 5, 245-281, (2015) · Zbl 1329.91111
[3] Atsalakis, G.; Nezis, D.; Matalliotakis, G.; Ucenic, C. I.; Skiadas, C., (2007)
[4] Brouhns, N.; Denuit, M.; Vermunt, J. K., A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance: Mathematics and Economics, 31, 373-393, (2002) · Zbl 1074.62524
[5] Cairns, A. J.C., Modelling and management of mortality risk: A review, Scandinavian Actuarial Journal, 2-3, 79-113, (2008) · Zbl 1224.91048
[6] Currie, I. D., On fitting generalized linear and non-linear models of mortality, Scandinavian Actuarial Journal, 4, 356-383, (2016) · Zbl 1401.91123
[7] Cox, D. R., Regression models and life tables (with discussion), Journal of the Royal Statistical Society, Series B., 34, 187-220, (1972) · Zbl 0243.62041
[8] Cybenko, G., Approximation by superpositions of a sigmoidal function, Mathematics of Control Signals Systems, 2, 303-314, (1989) · Zbl 0679.94019
[9] Dimitrova, D. S.; Haberman, S.; Kaishev, V. K., Dependent competing risks: Cause elimination and its impact on survival, Insurance: Mathematics and Economics, 53, 464-477, (2013) · Zbl 1304.91099
[10] Dong, D.; Mcavoy, T. J., Nonlinear principal component analysis—Based on principal curves and neural networks, Computers & Chemical Engineering, 20, 65-78, (1996)
[11] Fung, M. C.; Peters, G.; Shevchenko, P., (2015)
[12] Fung, M. C.; Peters, G.; Shevchenko, P., (2016)
[13] Fung, M. C.; Peters, G.; Shevchenko, P., (2017)
[14] Fotheringhame, D.; Baddeley, R., Nonlinear principal components analysis of neuronal spike train data, Biological Cybernetics, 77, 282-288, (1997) · Zbl 0887.92008
[15] Hainaut, D., Multidimensional Lee-Carter model with switching mortality processes, Insurance: Mathematics and Economics, 5, 236-246, (2012) · Zbl 1235.91091
[16] Hornik, K., Approximation capabilities of multilayer feedforward networks, Neural Networks, 4, 251-257, (1991)
[17] Khachaturyan, A.; Semenovskaya, S.; Vainshtein, B., Statistical-thermodynamic approach to determination of structure amplitude phases, Soviet Physics Crystallography, 24, 519-524, (1979)
[18] Kramer, M. A., Nonlinear principal component analysis using autoassociative neural networks, AIChE Journal, 37, 233-243, (1991)
[19] Lee, R. D.; Carter, L., Modelling and forecasting the time series of US mortality, Journal of the American Statistical Association, 87, 659-671, (1992)
[20] Lee, R. D., The Lee-Carter method for forecasting mortality, with various extensions and applications, North American Actuarial Journal, 4, 80-91, (2000) · Zbl 1083.62535
[21] Malthouse, E. C., Limitations of nonlinear PCA as performed with generic neural networks, IEEE Transaction on Neural Networks, 9, 165-173, (1998)
[22] Mcnelis, P. D., Neural Networks in Finance: Gaining Predictive Edge in the Market, (2005), Burlington, MA: Elsevier Academic Press, Burlington, MA
[23] Monahan, H. A., Nonlinear principal component analysis by neural networks: Theory and application to the Lorenz system, Journal of Climate, 13, 821-835, (2000)
[24] O’Hare, C.; Li, Y., Explaining young mortality, Insurance, Mathematics and Economics, 50, 12-25, (2012) · Zbl 1235.91102
[25] Pitacco, E., Survival models in a dynamic context: A survey, Insurance: Mathematics and Economics, 35, 279-298, (2004) · Zbl 1079.91050
[26] Pitacco, E.; Denuit, M.; Haberman, S.; Olivieri, A., Modeling Longevity Dynamics for Pensions and Annuity Business, (2009), London: Oxford University Press, London · Zbl 1163.91005
[27] Puddu, P. E.; Menotti, A., Artificial neural network versus multiple logistic function to predict 25-year coronary heart disease mortality in the Seven Countries, European Journal of Preventive Cardiology, 16, 583-591, (2009)
[28] Puddu, P. E.; Menotti, A., Artificial neural networks versus proportional hazards Cox models to predict 45-year all-cause mortality in the Italian rural areas of the seven countries study, BMC Medical Research Methodology, 12, 100, (2012)
[29] Puddu, P. E.; Piras, P.; Menotti, A., Lifetime competing risks between coronary heart disease mortality and other causes of death during 50 years of follow-up, International Journal of Cardiology, 228, 359-363, (2017)
[30] Renshaw, A. E.; Haberman, S., Lee-Carter mortality forecasting with age-specific enhancement, Insurance: Mathematics and Economics, 33, 255-272, (2003) · Zbl 1103.91371
[31] Renshaw, A.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570, (2006) · Zbl 1168.91418
[32] Toczydlowska, D.; Peters, G.; Fung, M. C.; Shevchenko, P. V., (2017)
[33] Van Berkum, F.; Antonio, K.; Vellekoop, M., The impact of multiple structural changes on mortality predictions, Scandinavian Actuarial Journal, 2016, 581-603, (2016) · Zbl 1401.91221
[34] Wilmoth, J. R., (1993)
[35] Wong-Fupuy, C.; Haberman, Projecting mortality trends: Recent developments in the UK and the US, North American Actuarial Journal, 8, 56-83, (2004) · Zbl 1085.62517
[36] Yang, S. S.; Yue, J. C.; Huang, H., Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models, Insurance: Mathematics and Economics, 46, 254-270, (2010) · Zbl 1231.91254
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