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A geostatistical approach for dynamic life tables: the effect of mortality on remaining lifetime and annuities. (English) Zbl 1231.91173

Summary: Dynamic life tables arise as an alternative to the standard (static) life table, with the aim of incorporating the evolution of mortality over time. The parametric model introduced by Lee and Carter in 1992 for projected mortality rates in the US is one of the most outstanding and has been used a great deal since then. Different versions of the model have been developed but all of them, together with other parametric models, consider the observed mortality rates as independent observations. This is a difficult hypothesis to justify when looking at the graph of the residuals obtained with any of these methods.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
86A32 Geostatistics

Software:

forecast; gnm; Forecast; R
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References:

[1] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1965), Dover New York · Zbl 0515.33001
[2] Benjamin, B.; Soliman, A., Mortality on the move, (1993), Actuarial Education Service Oxford
[3] Booth, H.; Maindonald, J.; Smith, L., Applying lee – carter under conditions of variable mortality decline, Population studies, 56, 3, 325-336, (2002)
[4] Brouhns, N.; Denuit, M.; Keilegom, I.V., Bootstrapping Poisson log-bilinear model for mortality forecasting, Scandinavian actuarial journal, 3, 212-224, (2005) · Zbl 1092.91038
[5] Cressie, N., Statistics for spatial data, (1993), John Wiley New York
[6] Cressie, N.; Majure, J., Spatio-temporal statistical modelling of livestock waste in streams, Journal of agricultural, biological, and environmental statistics, 2, 1, 24-47, (1997)
[7] Debón, A.; Montes, F.; Puig, F., Modelling and forecasting mortality in Spain, European journal of operation research, 189, 3, 624-637, (2008) · Zbl 1142.62419
[8] Debón, A.; Montes, F.; Sala, R., A comparison of parametric models for mortality graduation. application to mortality data of the Valencia region (Spain), Statistics and operations research transactions, 29, 2, 269-287, (2005) · Zbl 1274.62691
[9] Debón, A.; Montes, F.; Sala, R., A comparison of models for dynamical life tables. application to mortality data of the Valencia region (Spain), Lifetime data analysis, 12, 2, 223-244, (2006) · Zbl 1134.62369
[10] Debón, A.; Montes, F.; Sala, R., A comparison of nonparametric methods in the graduation of mortality: application to data from the Valencia region (Spain), International statistical review, 74, 2, 215-233, (2006) · Zbl 1134.62369
[11] Efron, B.; Tibshirani, R., An introduction to the boostrap, (1993), Chapman & Hall New York, London
[12] Felipe, A.; Guillén, M.; Pérez-Marín, A., Recent mortality trends in the Spanish population, British actuarial journal, 8, 4, 757-786, (2002)
[13] Forfar, D.; McCutcheon, J.; Wilkie, A., On graduation by mathematical formula, Journal of the institute of actuaries, 115, Part I(459), 1-149, (1988)
[14] Gavin, J.; Haberman, S.; Verrall, R., Moving weighted average graduation using kernel estimation, Insurance: mathematics & economics, 12, 2, 113-126, (1993) · Zbl 0778.62096
[15] Gavin, J.; Haberman, S.; Verrall, R., On the choice of bandwidth for kernel graduation, Journal of the institute of actuaries, 121, 119-134, (1994)
[16] Gavin, J.; Haberman, S.; Verrall, R., Graduation by kernel and adaptive kernel methods with a boundary correction, Transactions of the society of actuaries, XLVII, 173-209, (1995)
[17] Gneiting, T., Nonseparable, stationary covariance functions for space – time data, Journal of the American statistical association, 97, 590-600, (2002) · Zbl 1073.62593
[18] Guillen, M.; Vidiella-i-Anguera, A., Forecasting Spanish natural life expectancy, Risk analysis, 25, 5, 1161-1170, (2005)
[19] Hyndman, R.J., 2008. Forecast: forecasting functions for time series. R Package Version 1.11.
[20] Journel, A.G.; Huijbregts, C.J., Mining geostatistics, (1978), Academic Press New York
[21] Koissi, M.; Shapiro, A.; Högnäs, G., Evaluating and extending the lee – carter model for mortality forecasting confidence interval, Insurance: mathematics & economics, 38, 1, 1-20, (2006) · Zbl 1098.62138
[22] Lee, R., The lee – carter method for forecasting mortality, with various extensions and applications, North American actuarial journal, 4, 1, 80-91, (2000) · Zbl 1083.62535
[23] Lee, R.; Carter, L., Modelling and forecasting US mortality, Journal of the American statistical association, 87, 419, 659-671, (1992)
[24] Li, S.-H., Hardy, M., Tan, K., 2006. Uncertainty in mortality forecasting: an extension to the classical Lee-Carter approach. Technical Report. Waterloo University. · Zbl 1203.91113
[25] Martínez-Ruiz, F., 2008. Modelización de la función de covarianza en procesos espacio – temporales: análisis y aplicaciones. Ph.D. Thesis. Universitat de València. Spain.
[26] Mateu, J.; Montes, F.; Plaza, M., The 1970 US draft lottery revisited: a spatial analysis, Journal of the royal statistical society: series C (applied statistics), 53, 1, 219-229, (2004) · Zbl 1111.62394
[27] Matheron, G., Random sets and integral geometry, (1975), Wiley New York · Zbl 0321.60009
[28] Pedroza, C., A Bayesian forecasting model: predicting US male mortality, Biostatistics, 7, 4, 530-550, (2006) · Zbl 1170.62397
[29] Pitacco, E., Survival models in dynamic context: a survey, Insurance: mathematics & economics, 35, 2, 279-298, (2004) · Zbl 1079.91050
[30] R Development Core Team. 2005. R: a language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. ISBN: 3-900051-07-0.
[31] Renshaw, A., Actuarial graduation practice and generalised linear models, Journal of the institute of actuaries, 118, II, 295-312, (1991)
[32] Renshaw, A.; Haberman, S., Lee – carter mortality forecasting with age specific enhancement, Insurance: mathematics & economics, 33, 2, 255-272, (2003) · Zbl 1103.91371
[33] Renshaw, A.; Haberman, S., A cohort-based extension to the lee – carter model for mortality reduction factors, Insurance: mathematics & economics, 38, 3, 556-570, (2006) · Zbl 1168.91418
[34] Renshaw, A.; Haberman, S., On simulation-based approaches to risk measurement in mortality with specific reference to Poisson lee – carter modelling, Insurance: mathematics & economics, 42, 2, 797-816, (2008) · Zbl 1152.91598
[35] ()
[36] Turner, H., Firth, D., 2006. Generalized nonlinear models in R: an overview of the gnm package. R Package Version 0.9-1.
[37] Wong-Fupuy, C.; Haberman, S., Projecting mortality trends: recent developments in the united kingdom and the united states, North American actuarial journal, 8, 2, 56-83, (2004) · Zbl 1085.62517
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