Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-27T16:35:52.197Z Has data issue: false hasContentIssue false

A NEURAL-NETWORK ANALYZER FOR MORTALITY FORECAST

Published online by Cambridge University Press:  09 January 2018

Donatien Hainaut*
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Sciences, Unversité Catholique de Louvain, Voie du Roman Pays, 30 bte L1.04.01, 1348 Louvain La Neuve, Belgium
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Copyright © Astin Bulletin 2018 

References

Abdulkarim, S.A. and Garko, A.B. (2015) Forecasting maternal mortality rate using particle Swarm optimization based artificial neural network. Dutse Journal of Pure and Applied Sciences, 1 (1), 5559.Google Scholar
Antonio, K., Bardoutsos, A. and Ouburg, W. (2015) Bayesian Poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal, 5, 245281.Google Scholar
Atsalakis, G., Nezis, D., Matalliotakis, G., Ucenic, C.I. and Skiadas, C. (2007) Forecasting mortality rate using a neural network with fuzzy inference system. Working Paper n. 0806, University of Crete.Google Scholar
Brouhns, N., Denuit, M. and Vermunt, J.K. (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31 (3), 373393.Google Scholar
Cairns, A.J.C. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2–3, 79113.Google Scholar
Currie, I.D. (2016) On fitting generalized linear and non-linear models of mortality. Scandinavian Actuarial Journal, 4, 356383.Google Scholar
Cox, D.R. (1972) Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B., 34, 187220.Google Scholar
Cybenko, G. (1989) Approximation by superpositions of a sigmoidal function. Mathematics of Control Signals Systems, 2, 303314.Google Scholar
Dimitrova, D.S., Haberman, S. and Kaishev, V.K. (2013) Dependent competing risks: Cause elimination and its impact on survival. Insurance: Mathematics and Economics, 53, 464477.Google Scholar
Dong, D. and McAvoy, T.J. (1996) Nonlinear principal component analysis—Based on principal curves and neural networks. Computers & Chemical Engineering, 20, 6578.Google Scholar
Fung, M.C., Peters, G. and Shevchenko, P. (2015) A state-space estimation of the Lee-Carter mortality model and implications for annuity pricing. Available at SSRN: https://ssrn.com/abstract=2699624Google Scholar
Fung, M.C., Peters, G. and Shevchenko, P. (2016) A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting. Available at SSRN: https://ssrn.com/abstract=2786559Google Scholar
Fung, M.C., Peters, G. and Shevchenko, P. (2017) Cohort effects in mortality modelling: A Bayesian state-space approach. Available at SSRN: https://ssrn.com/abstract=2907868Google Scholar
Fotheringhame, D. and Baddeley, R. (1997) Nonlinear principal components analysis of neuronal spike train data. Biological Cybernetics, 77, 282288.Google Scholar
Hainaut, D. (2012) Multidimensional Lee–Carter model with switching mortality processes. Insurance: Mathematics and Economics, 5 (2), 236246.Google Scholar
Hornik, K. (1991) Approximation capabilities of multilayer feedforward networks. Neural Networks, 4 (2), 251257.Google Scholar
Khachaturyan, A., Semenovskaya, S. and Vainshtein, B. (1979) Statistical-thermodynamic approach to determination of structure amplitude phases. Soviet Physics Crystallography, 24 (5), 519524.Google Scholar
Kramer, M.A. (1991) Nonlinear principal component analysis using autoassociative neural networks. AIChE Journal, 37, 233243.Google Scholar
Lee, R.D. and Carter, L. (1992) Modelling and forecasting the time series of US mortality. Journal of the American Statistical Association, 87, 659671.Google Scholar
Lee, R.D. (2000) The Lee–Carter method for forecasting mortality, with various extensions and applications. North American Actuarial Journal, 4 (1), 8091.Google Scholar
Malthouse, E.C. (1998) Limitations of nonlinear PCA as performed with generic neural networks. IEEE Transaction on Neural Networks, 9, 165173.Google Scholar
McNelis, P.D. (2005) Neural Networks in Finance: Gaining Predictive Edge in the Market. Burlington, MA: Elsevier Academic Press.Google Scholar
Monahan, H.A. (2000) Nonlinear principal component analysis by neural networks: Theory and application to the Lorenz system. Journal of Climate, 13, 821835.Google Scholar
O'Hare, C. and Li, Y. (2012) Explaining young mortality. Insurance, Mathematics and Economics, 50, 1225.Google Scholar
Pitacco, E. (2004) Survival models in a dynamic context: A survey. Insurance: Mathematics and Economics, 35, 279298.Google Scholar
Pitacco, E., Denuit, M., Haberman, S. and Olivieri, A. (2009) Modeling Longevity Dynamics for Pensions and Annuity Business. London: Oxford University Press.CrossRefGoogle Scholar
Puddu, P.E. and Menotti, A. (2009) 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 (5), 583591.Google Scholar
Puddu, P.E. and Menotti, A. (2012) 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.Google Scholar
Puddu, P.E., Piras, P. and Menotti, A. (2017) Lifetime competing risks between coronary heart disease mortality and other causes of death during 50 years of follow-up. International Journal of Cardiology, 228, 359363.Google Scholar
Renshaw, A.E. and Haberman, S. (2003) Lee–Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255272.Google Scholar
Renshaw, A. and Haberman, S. (2006) A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556570.Google Scholar
Toczydlowska, D., Peters, G., Fung, M.C. and Shevchenko, P.V. (2017) Stochastic period and cohort effect state-space mortality models incorporating demographic factors via probabilistic robust principle components. Available at SSRN: https://ssrn.com/abstract=2977306Google Scholar
Van Berkum, F., Antonio, K. and Vellekoop, M. (2016) The impact of multiple structural changes on mortality predictions. Scandinavian Actuarial Journal, 2016 (7), 581603.Google Scholar
Wilmoth, J.R. (1993) Computational methods for fitting and extrapolating the Lee–Carter model of mortality change. Technical Report, Department of Demography, University of California, Berkeley.Google Scholar
Wong-Fupuy, C. and Haberman, (2004) Projecting mortality trends: Recent developments in the UK and the US. North American Actuarial Journal, 8, 5683.Google Scholar
Yang, S.S., Yue, J.C. and Huang, H. (2010) Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics 46 (1), 254270.Google Scholar