Understanding patterns of mortality homogeneity and heterogeneity across countries and their role in modeling mortality dynamics and hedging longevity risk. (English) Zbl 1465.91098

The authors propose a methodology, based on the graduation method, to detect differences in mortality rates across different populations. Using an index \(h^2\) based on the partial standard mortality ratio, they measure mortality homogeneity and heterogeneity, then conduct an empirical study across countries with emerging and developed markets.
The results of model fitting show that it is inappropriate to use a coherent mortality model for the mortality-heterogeneous populations. It is shown that information concerning mortality homogeneity/heterogeneity can be used for pooling risk in insurance and increasing overall hedge effectiveness.


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


[1] Brillinger, D. R., The natural variability of vital rates and associated statistics, Biometrics, 42, 693-734 (1986) · Zbl 0611.62136
[2] Hatzopoulos, P.; Haberman., S., Common mortality modelling and coherent forecasts. An empirical analysis of worldwide mortality data, Insurance: Mathematics and Economics, 52, 320-37 (2013) · Zbl 1284.91238
[3] Koissi, M. C.; Shapiro, A. F.; Högnäs., G., Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval, Insurance: Mathematics and Economics, 26, 1-20 (2006) · Zbl 1098.62138
[4] Lee, R., The Lee-Carter method for forecasting mortality, with various extensions and applications, North American Actuarial Journal, 4, 80-91 (2000) · Zbl 1083.62535
[5] Lee, R. D.; Carter., L. R., Modeling and forecasting the time series of U.S. mortality, Journal of the American Statistical Association, 87, 659-71 (1992) · Zbl 1351.62186
[6] Lee, R. D.; Nault, F., Modeling and forecasting provincial mortality in Canada. Paper presented at the World Congress of the International Union for the Scientific Study of Population (1993), Montreal, Canada
[7] Lee, W. C., A partial SMR approach to smoothing age-specific rates, Annals of Epidemiology, 13, 89-99 (2003)
[8] Li, J., A Poisson common factor model for projecting mortality and life expectancy jointly for females and males, Population Studies, 67, 111-26 (2013)
[9] Li, J. S. H.; Hardy., M. R., Measuring basis risk in longevity hedges, North American Actuarial Journal, 15, 177-200 (2011) · Zbl 1228.91042
[10] Li, N.; Lee., R., Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography, 42, 575-94 (2005)
[11] Milidonis, A., Multi-population mortality risk in Asia-Pacific: Insurance Risk and Finance Research Centre technical report (2015)
[12] Renshaw, A. E.; Haberman., S., On the forecasting of mortality reduction factors, Insurance: Mathematics and Economics, 32, 379-401 (2003) · Zbl 1025.62041
[13] 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
[14] Russolillo, M.; Giordano, G.; Haberman., S., Extending the Lee-Carter model: A three-way decomposition,, Scandinavian Actuarial Journal, 2, 96-117 (2011) · Zbl 1277.62260
[15] Tuljapurkar, S.; Li, N.; Boe., C., A universal pattern of mortality decline in the G7 countries, Nature, 405, 789-92 (2000)
[16] Villegas, A.; Haberman., S., On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England, North American Actuarial Journal, 18, 1, 168-93 (2014) · Zbl 1412.91057
[17] White, K. M., Longevity advances in high-income countries, 1955-96, Population and Development Review, 28, 59-76 (2002)
[18] Wilson, C., On the scale of global demographic convergence 1950-2000, Population and Development Review, 27, 155-72 (2001)
[19] Yang, S. S.; Chang, Y.-P.; Yeh, Y.-Y., A residual bootstrapped analysis of Lee-Carter model in mortality forecasting, . 12th APRIA Annual Conference (2008)
[20] Yue, J. C.; Yang, S. S.; Yeh, Y.-Y., Modeling longevity risk for small populations under a coherent framework (2015)
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.