Modeling and forecasting mortality rates. (English) Zbl 1284.91259

Summary: We show that by modeling the time series of mortality rate changes rather than mortality rate levels we can better model human mortality. Leveraging on this, we propose a model that expresses log mortality rate changes as an age group dependent linear transformation of a mortality index. The mortality index is modeled as a Normal Inverse Gaussian. We demonstrate, with an exhaustive set of experiments and data sets spanning 11 countries over 100 years, that the proposed model significantly outperforms existing models. We further investigate the ability of multiple principal components, rather than just the first component, to capture differentiating features of different age groups and find that a two component NIG model for log mortality change best fits existing mortality rate data.


91B30 Risk theory, insurance (MSC2010)
91B84 Economic time series analysis
91D20 Mathematical geography and demography
62M20 Inference from stochastic processes and prediction
Full Text: DOI


[1] Booth, H.; Hyndman, R.; Tickle, L.; Jong, P. D., Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions, Demographic Research, 15, 289-310, (2006)
[2] Cairns, A.; Blake, D.; Dowd, K.; Coughlan, G.; Epstein, D.; Khalaf-Allah, M., Mortality density forecasts: an analysis of six stochastic mortality models, Insurance: Mathematics & Economics, 48, 355-367, (2011)
[3] Chen, H.; Cox, S., Modeling mortality with jumps: applications to mortality securitization, The Journal of Risk and Insurance, 76, 3, 727-751, (2009)
[4] Couzin-Frankel, J., A pitched battle over life span, Science, 29, 549-550, (2011)
[5] DeJong, P.; Tickle, L., Extending Lee-Carter mortality forecasting, Mathematical Population Studies, 13, 1, 1-18, (2006) · Zbl 1151.91742
[6] de Moivre, A., Annuities upon lives, (1725), W.P. Fayram
[7] Deng, Y.; Brockett, P.; MacMinn, R., Longevity/mortality risk modeling and securities pricing, Journal of Risk and Insurance, 79, 3, 697-721, (2012)
[8] Gavrilov, L.; Gavrilova, N., Mortality measurement at advanced ages: a study of the social security administration death master file, North American Actuarial Journal, 15, 432-447, (2011)
[9] Girosi, F., King, G., 2007. Understanding the Lee-Carter mortality forecasting method. URL gking.harvard.edu/files/lc.pdf.
[10] Gompertz, B., On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philosophical Transactions of the Royal Society of London, 115, 513-585, (1825)
[11] Graunt, J., 1662. Natural and political observations made upon the bills of mortality.
[12] Haberman, S.; Renshaw, A., A comparative study of parametric mortality projection models, Insurance: Mathematics & Economics, 48, 35-55, (2011)
[13] Haberman, S.; Renshaw, A., Parametric mortality improvement rate modeling and projecting, Insurance: Mathematics & Economics, 50, 309-333, (2012) · Zbl 1237.91129
[14] Halley, E., An estimate of the degrees of the mortality of mankind, drawn from curious tables of the births and funerals at the city of breslaw; with an attempt to ascertain the price of annuities upon lives, Philosophical Transactions of the Royal Society of London, 17, 596-610, (1693)
[15] Halonen, D., January 22, 2007. IRS sets costly table. Pension and Investments.
[16] Hollmann, F., Mulder, T., Kallan, J., 2000. Methodology and assumptions for the population projections of the United States: 1999 to 2100. Population Division, U.S. Bureau of Census 38.
[17] Human Mortality Database, 2011. University of California, Berkeley (USA), and Max Plank Institute for Demographic Research (Germany). URL www.mortality.org.
[18] Janssen, F.; Kunst, A., Cohort patterns in mortality trends among the elderly in seven European countries, 1950-99, International Journal of Epidemiology, 34, 1149-1159, (2005)
[19] Jolliffe, I., Principal component analysis, (2002), Springer New York · Zbl 1011.62064
[20] Kou, S.; Wang, H., Option pricing under a double exponential jump diffusion model, Management Science, 50, 9, 1178-1192, (2004)
[21] Lee, R.; Carter, L., Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 419, 659-671, (1992) · Zbl 1351.62186
[22] Li, J.; Chan, W.; Cheung, S., Structural changes in the Lee-Carter mortality indexes: detection and implications, North American Actuarial Journal, 15, 1, 13-31, (2011)
[23] Michael, J.; Schucany, W.; Haas, Roy, Generating random variates using transformations with multiple roots, The American Statistician, 30, 88-90, (1976) · Zbl 0331.65002
[24] Pension Capital Strategies, Jardine Lloyd Thompson, 2006. Pension capital strategies releases report on FTSE100 pension disclosures. URL www.jltgroup.com/content/UK/employee_benefits/pressreleases/070117PCSQuaReport.pdf.
[25] Plat, R., On stochastic mortality modeling, Insurance: Mathematics & Economics, 45, 393-404, (2009) · Zbl 1231.91227
[26] Renshaw, A.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics & Economics, 38, 556-570, (2006) · Zbl 1168.91418
[27] Reuters News Service, November 23, 2010. UK pension liabilities spike as people live longer. URL www.reuters.com/article/idUSLNE6AO01120101125.
[28] Wang, C.; Huang, H.; Liu, I., A quantitative comparison of the Lee-Carter model under different types of non-Gaussian innovations, The Geneva Papers, 36, 675-696, (2011)
[29] Yang, S.; Yue, J.; Huang, H., Modeling longevity risks using a principal component approach: a comparison with existing stochastic mortality models, Insurance: Mathematics & Economics, 46, 254-270, (2010) · Zbl 1231.91254
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.