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DIFFERENCES IN EUROPEAN MORTALITY RATES: A GEOMETRIC APPROACH ON THE AGE–PERIOD PLANE

Published online by Cambridge University Press:  03 July 2015

Marcus C. Christiansen ,
Evgeny Spodarev  and
Verena Unseld
Marcus C. Christiansen*
Affiliation:
Maxwell Institute for Mathematical Sciences, Edinburgh, and Heriot-Watt University, Edinburgh, UK
Evgeny Spodarev
Affiliation:
Institute of Stochastics, Ulm University, Germany E-Mail: [email protected]
Verena Unseld
Affiliation:
Institute of Stochastics, Ulm University, Germany E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

Age and period are the most widely used parameters for forecasting mortality rates. Empirical mortality rate differences in multiple populations often show strong geometric patterns on the two-dimensional age–period plane. The idea of this paper is to take these geometric patterns as the starting point for the development of forecasts. A parametric approach is presented and discussed which uses simple techniques from spatial statistics. The proposed model is statistically parsimonious and yields forecasts that are consistent with the historical data and coherent for multiple populations.

Keywords

Mortality forecastingmodeling multiple populationsBox–Cox transformgeostatisticsGaussian random fieldsconditional simulationKriging
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 3 , September 2015 , pp. 477 - 502
Copyright
Copyright © Astin Bulletin 2015 

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References

Ahcan, A., Medved, D., Olivieri, A. and Pitacco, E. (2014) Forecasting mortality for small populations by mixing mortality data. Insurance: Mathematics and Economics, 54, 12–27.Google Scholar
Börger, M. and Aleksic, M.-C. (2014) Coherent projections of age, period, and cohort dependent mortality improvements. Society of Actuaries Living to 100 Symposium, Orlando, USA.Google Scholar
Börger, M., Fleischer, D. and Kuksin, N. (2014) Modeling the mortality trend under modern solvency regimes. ASTIN Bulletin, 44 (1), 1–38.CrossRefGoogle Scholar
Box, G.E.P. and Cox, D.R. (1964) An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), 26 (2), 211–252.CrossRefGoogle Scholar
Cairns, A., Blake, D., Dowd, K., Coughlan, G. and Khalaf-Allah, M. (2011) Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41 (1), 29–59.Google Scholar
Chilès, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling spatial Uncertainty. Wiley Series in Probability and Statistics: Applied Probability and Statistics. New York: John Wiley & Sons, Inc.CrossRefGoogle Scholar
Cressie, N.A.C. (1993) Statistics for Spatial Data, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York: John Wiley & Sons, Inc.CrossRefGoogle Scholar
Debón, A., Martínez-Ruiz, F. and Montes, F. (2010) A geostatistical approach for dynamic life tables: the effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47, 327–336.Google Scholar
Dietrich, C.R. and Newsam, G.N. (1997) Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix. SIAM Journal on Scientific Computing, 18 (4), 1088–1107.CrossRefGoogle Scholar
Fahrmeir, L., Kneib, T., Lang, S. and Marx, B. (2013) Regression: Models, Methods and Applications. Heidelberg: Springer.CrossRefGoogle Scholar
Hyndman, R., Booth, H. and Yasmeen, F. (2012) Coherent mortality forecasting: the product-ratio method with functional time series models. Demography, 50 (1), 261–283.CrossRefGoogle Scholar
Jarner, S.F. and Kryger, E.M. (2011) Modelling adult mortality in small populations: the saint model. ASTIN Bulletin, 41 (2), 377–418.Google Scholar
Lantuejoul, C. (2012) Geostatistical Simulation: Models and Algorithms. Berlin: Springer.Google Scholar
Li, J. and Hardy, M. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15 (2), 177–200.CrossRefGoogle 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
Spodarev, E. (ed.) (2013) Stochastic Geometry, Spatial Statistics and Random Fields: Asymptotic Methods, Lecture Notes in Mathematics, volume 2068. Berlin: Springer.CrossRefGoogle Scholar
Spodarev, E., Shmileva, E. and Roth, S. (2015) Extrapolation of stationary random fields. In Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms (ed. Schmidt, V.) Lecture Notes in Mathematics, volume 2120, pp. 321–368. Berlin: Springer.CrossRefGoogle Scholar
University of California and Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). (2014) The human mortality database. Available at: http://www.mortality.org (2014.01.15).Google Scholar
Wackernagel, H. (1995) Multivariate Geostatistics. An Introduction with Applications, 2nd edn.Berlin: Springer.CrossRefGoogle Scholar
Wilmoth, J.R.et al. (2007) Methods protocol for the human mortality database. Available at: http://www.mortality.org/Public/Docs/MethodsProtocol.pdf (2015.02.07).Google Scholar