A synthesis mortality model for the elderly. (English) Zbl 1461.91261

Summary: Mortality improvement has been a common phenomenon since the 20th century, and the human longevity continues to prolong. Postretirement life receives a lot of attention, and modeling mortality rates of the elderly (ages 65 years and beyond) is essential because life expectancy has reached the highest level in history. Mortality models can be divided into two groups, relational and stochastic models, but there is no consensus on which model is better in modeling mortality rates of the elderly. In this study, instead of choosing either a relational or stochastic model, we propose a synthesis model, selecting and modifying appropriate models from both groups, which not only has a satisfactory estimation result but also can be used for mortality projection. We use the data from the United States, the United Kingdom, Japan, and Taiwan (data were from the Human Mortality Database) to evaluate the proposed approach. We found that the proposed model performs well and is a possible choice for modeling mortality rates of the elderly.


91G05 Actuarial mathematics
91D20 Mathematical geography and demography
Full Text: DOI


[1] Ahcan, A.; Medved, D.; Olivieri, A.; Pitacco, E., Forecasting mortality for small populations by mixing mortality data, Insurance: Mathematics and Economics, 54, 12-27 (2014)
[2] Akaike, H.; Petrov, B. N.; Csaki, F., Proceedings of the Second International Symposium on Information Theory, Information theory and an extension of the maximum likelihood principle, 267-81 (1973), Budapest, Hungary: Akademiai Kiado, Budapest, Hungary
[3] Bohk-Ewald, C.; Rau., R., Probabilistic mortality forecasting with varying age specific survival improvements, Genus, 73, 1, 1-37 (2017)
[4] Bőrger, M.; Schupp., J., Modeling trend processes in parametric mortality models, Insurance: Mathematics and Economics, 78, 369-80 (2018) · Zbl 1400.91241
[5] Brouhns, N.; Denuit, M.; Vermunt., J. K., A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance: Mathematics and Economics, 31, 373-93 (2002) · Zbl 1074.62524
[6] Brown, R. L., Introduction to the mathematics of demography (1993), New Hartford, CT: ACTEX, New Hartford, CT
[7] Burnham, K. P.; Anderson., D. R., Model selection and multimodel inference: A practical information-theoretic approach (2002), New York: Springer-Verlag · Zbl 1005.62007
[8] Cadena, M.; Denuit., M., Semi-parametric accelerated hazard relational models with applications to mortality projections, Insurance: Mathematics and Economics, 68, 1-16 (2016) · Zbl 1373.62513
[9] Cairns, A. J. G.; Blake, D.; Dowd., K., A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 687-718 (2006)
[10] Cairns, A. J. G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Epstein, D.; Ong, A.; Balevich., I., A quantitative comparison of stochastic mortality models using data from England and Wales and the United States, North American Actuarial Journal, 13, 1-35 (2009)
[11] Carnes, B. A.; Olshansky, S. J.; Grahn., D., Discussed biological evidence for limits to the duration of life, Biogeography, 4, 1, 31-45 (2003)
[12] Chen, H.; Cox., S. H., Modeling mortality with jumps: Applications to mortality securitization, Journal of Risk and Insurance, 76, 727-51 (2009)
[13] Coale, A.; Kisker, E. E., Defects in data on old-age mortality in the United States: New procedures for calculating mortality schedules and life tables at the highest ages, Asian and Pacific Population Forum, 4, 1, 1-31 (1990)
[14] Cox, S. H.; Lin, Y.; Pedersen., H., Mortality risk modeling: Applications to insurance securitization, Insurance: Mathematics and Economics, 46, 242-53 (2010) · Zbl 1231.91168
[15] Dowd, K.; Cairns, A. J. G.; Blake, D.; Coughlan, G. D.; Epstein, D.; Khalaf-Allah., M., Backtesting stochastic mortality models: An ex post evaluation of multiperiod-ahead density forecasts, North American Actuarial Journal, 14, 281-98 (2010)
[16] Haberman, S.; Renshaw., A., On age-period-cohort parametric mortality rate projections, Insurance: Mathematics and Economics, 45, 255-270 (2009) · Zbl 1231.91195
[17] Kannisto, V., Odense Monographs on Population Aging, 1, Development of oldest-old mortality, 1950-1990: Evidence from 28 developed countries (1994), Odense, Denmark: Odense University Press, Odense, Denmark
[18] Kannisto, V.; Lauritsen, J.; Thatcher, A. R.; Vaupel., J. W., Reductions in mortality at advanced ages: Several decades of evidence from 27 countries, Population and Development Review, 20, 4, 793-810 (1994)
[19] Lee, R. D.; Carter., L. R., Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 419, 659-71 (1992) · Zbl 1351.62186
[20] Lee, W., A partial SMR approach to smoothing age-specific rates, Annuals of Epidemiology, 13, 2, 89-99 (2003)
[21] Li, J. S.-H., Uncertainty in mortality forecasting: An extension to the classical Lee-Carter approach, Astin Bulletin, 39, 137-64 (2009) · Zbl 1203.91113
[22] Li, J. S.-H.; Chan,, W.; Cheung., S., Structural changes in the Lee-Carter mortality indexes: Detection and implications, North American Actuarial Journal, 15, 13-31 (2011)
[23] Mitchell, D.; Brockett, P.; Mendoza-Arriaga, R.; Muthuraman., K., Modeling and forecasting mortality rates, Insurance: Mathematics and Economics, 52, 275-85 (2013) · Zbl 1284.91259
[24] Renshaw, A. E.; Haberman., S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-70 (2006) · Zbl 1168.91418
[25] Perks, W., On some experiments in the graduation of mortality statistics, Journal of the Institute of Actuaries, 63, 12-40 (1932)
[26] Preston, S. H.; Stokes., A., Sources of population aging in more and less developed countries, Population and Development Review, 38, 2, 221-36 (2012)
[27] Terblanche, W., Retrospective testing of mortality forecasting methods for the projection of very elderly populations in Australia, Journal of Forecasting, 35, 703-17 (2016)
[28] Thatcher, A. R.; Kannisto, V.; Vaupel., J. W., Odense Monographs on Population Aging, 5, The force of mortality at ages 80 to 120 (1999), Odense, Denmark: Odense University Press, Odense, Denmark
[29] Thatcher, A. R.; Kannisto, V.; Andreev., K., The survivor ratio method for estimating numbers at high ages, Demographic Research, 6, 1, 2-15 (2002)
[30] Tsai, C. C. L.; Yang., S., A linear regression approach to modeling mortality rates of different forms, North American Actuarial Journal, 19, 1-23 (2015) · Zbl 1414.91238
[31] Tsai, C. C. L.; Lin., T., Incorporating the Bühlmann credibility into mortality models to improve forecasting performances, Scandinavian Actuarial Journal, 2017, 5, 419-40 (2017) · Zbl 1401.91198
[32] Van Berkum, F., The impact of multiple structural changes on mortality predictions, Scandinavian Actuarial Journal, 2016, 581-603 (2016) · Zbl 1401.91221
[33] Wang, H.; Yue, C. J.; Chen, Y., A study of elderly mortality models, Journal of Population Studies, 52, 1-42 (2016)
[34] Wang, H.; Yue, C. J.; Chong., C., Mortality models and longevity risk for small populations, Insurance: Mathematics and Economics, 78, 351-59 (2018) · Zbl 1400.91254
[35] Yue, C. J., Oldest-old mortality rates and the Gompertz law: A theoretical and empirical study based on four countries, Journal of Population Studies, 24, 33-57 (2002)
[36] Yue, C. J., Mortality compression and longevity risk, North American Actuarial Journal, 16, 4, 434-48 (2012)
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.