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CALIBRATING THE LEE-CARTER AND THE POISSON LEE-CARTER MODELS VIA NEURAL NETWORKS

Published online by Cambridge University Press:  31 March 2022

Salvatore Scognamiglio
Salvatore Scognamiglio*
Affiliation:
Department of Management and Quantitative Sciences University of Naples “Parthenope”Naples, Italy
*
E-mail: [email protected]
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Abstract

This paper introduces a neural network (NN) approach for fitting the Lee-Carter (LC) and the Poisson Lee-Carter model on multiple populations. We develop some NNs that replicate the structure of the individual LC models and allow their joint fitting by simultaneously analysing the mortality data of all the considered populations. The NN architecture is specifically designed to calibrate each individual model using all available information instead of using a population-specific subset of data as in the traditional estimation schemes. A large set of numerical experiments performed on all the countries of the Human Mortality Database shows the effectiveness of our approach. In particular, the resulting parameter estimates appear smooth and less sensitive to the random fluctuations often present in the mortality rates’ data, especially for low-population countries. In addition, the forecasting performance results significantly improved as well.

Keywords

Mortality modellingmulti-population mortality modellingneural networksLee–Carter modelHuman Mortality Database
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 2 , May 2022 , pp. 519 - 561
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

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References

Alho, J.M. (2000) Discussion of Lee (2000). North American Actuarial Journal, 4(1), 91–93.CrossRefGoogle Scholar
Barrieu, P., Bensusan, H., El Karoui, N., Hillairet, C., Loisel, S., Ravanelli, C. and Salhi, Y. (2012) Understanding, modelling and managing longevity risk: Key issues and main challenges. Scandinavian Actuarial Journal, 3, 203–231.CrossRefGoogle Scholar
Bengio, Y., Ducharme, R., Vincent, P. and Jauvin, C. (2003) A neural probabilistic language model. Journal of Machine Learning Research, 3, 1137–1155.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), 373–393.Google Scholar
Cairns, A.J., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk & Insurance, 73(4), 687–718.CrossRefGoogle Scholar
Cairns, A.J., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. and Balevich, I. (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1–53.CrossRefGoogle Scholar
Camarda, C.G. and Basellini, U. (2021) Smoothing, decomposing and forecasting mortality rates. European Journal of Population, 37(3), 1–34.CrossRefGoogle ScholarPubMed
Chollet, F. (2018) Keras: The Python deep learning library. Astrophysics Source Code Library.Google Scholar
Currie, I.D. (2013) Smoothing constrained generalized linear models with an application to the Lee-Carter model. Statistical Modelling, 13(1), 69–93.CrossRefGoogle Scholar
Delwarde, A., Denuit, M. and Eilers, P. (2007) Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting: A penalized log-likelihood approach. Statistical Modelling, 7(1), 29–48.CrossRefGoogle Scholar
Enchev, V., Kleinow, T. and Cairns, A.J. (2017) Multi-population mortality models: Fitting, forecasting and comparisons. Scandinavian Actuarial Journal, 4, 319–342.CrossRefGoogle Scholar
Goodfellow, I., Bengio, Y. and Courville, A. (2016) Deep Learning. Cambridge, MA: MIT Press.Google Scholar
Guo, C. and Berkhahn, F. (2016) Entity embeddings of categorical variables. arXiv:1604.06737.Google Scholar
Hainaut, D. (2018) A neural-network analyzer for mortality forecast. ASTIN Bulletin: The Journal of the IAA, 48(2), 481–508.CrossRefGoogle Scholar
Hainaut, D. and Denuit, M. (2020) Wavelet-based feature extraction for mortality projection. ASTIN Bulletin: The Journal of the IAA, 50(3), 675–707.CrossRefGoogle Scholar
Hyndman, R.J. and Ullah, M.S. (2007) Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics & Data Analysis, 51(10), 4942–4956.Google Scholar
Hunt, A. and Blake, D. (2017) Modelling mortality for pension schemes. ASTIN Bulletin: The Journal of the IAA, 47(2), 601–629.CrossRefGoogle Scholar
Jarner, S.F. and Kryger, E.M. (2011) Modelling adult mortality in small populations: The SAINT model. ASTIN Bulletin: The Journal of the IAA, 41(2), 377–418.Google Scholar
Kingma, D.P. and Ba, J. (2014) Adam: A method for stochastic optimization. arXiv:1412.6980.Google Scholar
Kleinow, T. (2015) A common age effect model for the mortality of multiple populations. Insurance: Mathematics and Economics, 63, 147–152.Google Scholar
LeCun, Y., Boser, B.E., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W.E. and Jackel, L.D. (1990) Handwritten digit recognition with a back-propagation network. Advances in Neural Information Processing Systems, 1(4), 396–404.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modelling and forecasting us mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Li, N. and Lee, R. (2005) Coherent mortality forecasts for a group of populations: An extension of the Lee–Carter method. Demography, 42(3), 575–594.CrossRefGoogle ScholarPubMed
Li, J.S.H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.CrossRefGoogle Scholar
Lindholm, M. and Palmborg, L. (2021) Effient use of data for LSTM mortality forecasting. online version.CrossRefGoogle Scholar
Nigri, A., Levantesi, S., Marino, M., Scognamiglio, S. and Perla, F. (2019) A deep learning integrated Lee–Carter model. Risks, 7(1), 33.CrossRefGoogle Scholar
Perla, F., Richman, R., Scognamiglio, S. and Wüthrich, M.V. (2021) Time-series forecasting of mortality rates using deep learning. Scandinavian Actuarial Journal, 7, 1–27.Google Scholar
Pham, V., Bluche, T., Kermorvant, C. and Louradour, J. (2014) Dropout improves recurrent neural networks for handwriting recognition. 14th International Conference on Frontiers in Handwriting Recognition IEEE, pp. 285–290.CrossRefGoogle Scholar
Renshaw, A.E. and Haberman, S. (2003a) Lee–Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33(2), 255–272.Google Scholar
Renshaw, A.E. and Haberman, S. (2003b) On the forecasting of mortality reduction factors. Insurance: Mathematics and Economics, 32(3), 379–401.Google Scholar
Renshaw, A.E. and Haberman, S. (2006) A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556–570.Google Scholar
Richman, R. (2020a). AI in actuarial science – a review of recent advances – part 1. Annals of Actuarial Science, 15(2), 207–229.CrossRefGoogle Scholar
Richman, R. (2020b) AI in actuarial science – a review of recent advances – part 2. Annals of Actuarial Science, 15(2), 230–258.CrossRefGoogle Scholar
Richman, R. and Wüthrich, M.V. (2021) A neural network extension of the Lee–Carter model to multiple populations. Annals of Actuarial Science , 15(2), 346–366.CrossRefGoogle Scholar
Richman, R. (2021) Mind the Gap-Safely Incorporating Deep Learning Models into the Actuarial Toolkit. Available at SSRN id=3857693.CrossRefGoogle Scholar
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I. and Salakhutdinov, R. (2014) Dropout: A simple way to prevent neural networks from overfitting. The Journal of Machine Learning Research, 15(1), 1929–1958.Google Scholar
Villegas, A.M., Haberman, S., Kaishev, V.K. and Millossovich, P. (2017) A comparative study of two population models for the assessment of basis risk in longevity hedges. ASTIN Bulletin: The Journal of the IAA, 47(3), 631–679.CrossRefGoogle Scholar
Villegas, A.M., Millossovich, P. and Kaishev, V.K. (2018) StMoMo: Stochastic mortality modeling in R. Journal of Statistical Software 84, 1–32.CrossRefGoogle Scholar
Wang, C.W., Zhang, J. and Zhu, W. (2020) Neighbouring prediction for mortality. ASTIN Bulletin: The Journal of the IAA, 51(3), 689–718.CrossRefGoogle Scholar