Abstract
An integral part of our model is the modelling of longevity as an essential part of the Solvency Capital Requirement. It is necessary to forecast future values of the probability of death and survival for each age in each future year. Our forecasts follow the methodology designed by the Austrian Actuarial Association published in Kainhofer et al. (2006, The new Austrian annuity valuation table AVÖ 2005R), which was inspired by the methodology designed by the German Association of Actuaries published in Pasdika et al. (2005, Coping with longevity: The new German annuity valuation table DAV 2004R). The approach is divided into two main parts: adult age modelling and old-age modelling. Each age interval is forecast with a different model and with different assumptions, as the number of observations available at each age is different.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R.E. Beard, Appendix: Note on some mathematical mortality models, in Ciba Foundation Symposium-The Lifespan of Animals (Colloquia on Ageing), Volume 5 (Wiley Online Library, 1959), pp. 302–311
N. Brouhns, M. Denuit, J.K. Vermunt, A Poisson log-bilinear regression approach to the construction of projected lifetables. Insur. Math. Econ. 31(3), 373–393 (2002)
B. Burcin, K. Tesárková, L. Šídlo, The most used balancing methods a extrapolation of the mortality curve and their application to the Czech population. Revue for research on population development. In Czech: Nejpoužívanejší metody vyrovnávání a extrapolace krivky úmrtnosti a jejich aplikace na ceskou populaci. Revue pro výzkum populačního vývoje 52, 77–89 (2010)
A.J.G. Cairns, D. Blake, K. Dowd, Pricing death: Frameworks for the valuation and securitization of mortality risk. Astin Bulletin 36(1), 79 (2006)
B. Gompertz, 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. Roy. Soc. Lond. Philos. Trans. I 115, 513–583 (1825)
Human Mortality Database, University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany), 2019. https://www.mortality.org. Online; Accessed 10 Sept 2019
R.J. Hyndman, Y. Khandakar, Automatic time series forecasting: the forecast package for R. J. Stat. Softw. 26(3), 1–22 (2008). http://www.jstatsoft.org/article/view/v027i03
R.J. Hyndman, H. Booth, L. Tickle, J. Maindonald, Demography: Forecasting mortality, fertility, migration and population data (2019). https://CRAN.R-project.org/package=demography. R package version 1.22
R. Kainhofer, M. Predota, U. Schmock, The new Austrian annuity valuation table AVÖ 2005R, (2006). http://www.avoe.at/pdf/mitteilungen/H13_w3.pdf
F. Koschin, How high is the intensity of mortality at the end of human life. In Czech: Jak vysoká je intenzita úmrtnosti na konci lidského života. Demografie 41(2), 105–119 (1999)
R.D. Lee, L.R. Carter, Modelling and Forecasting U.S. Mortality (1992). http://pagesperso.univ-brest.fr/~ailliot/doc_cours/M1EURIA/regression/leecarter.pdf. Online; Accessed 2 Oct 2019
Mortality Tables, Statistical Office of the Slovak Republic (2019). https://www.statistics.sk. Online; Accessed 10 Sept 2019
M.D. Pascariu, MortalityLaws: Parametric mortality models, life tables and HMD (2019). https://CRAN.R-project.org/package=MortalityLaws. R package version 1.8.0
U. Pasdika, J. Wolff, G. Re, M. Life, Coping with longevity: The new German annuity valuation table DAV 2004 R, in The living to 100 and beyond symposium, Orlando Florida, vol. 2, p. 6 (2005)
R Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2018). https://www.R-project.org/
A.R. Thatcher, The long-term pattern of adult mortality and the highest attained age. J. R. Stat. Soc, A (Stat. Soc.) 162(1), 5–43 (1999)
A.R. Thatcher, V. Kannisto, J.W. Vaupel, et al., The force of mortality at ages 80 to 120, vol. 22 (Odense University Press Odense, 1998)
A.M. Villegas, V.K. Kaishev, P. Millossovich, StMoMo: An R package for stochastic mortality modeling. J. Stat. Softw. 84(3), 1–38 (2018). https://doi.org/10.18637/jss.v084.i03
J.R. Wilmoth, K. Andreev, D. Jdanov, D.A. Glei, C. Boe, M. Bubenheim, D. Philipov, V. Shkolnikov, P. Vachon, Methods protocol for the human mortality database [version 31/05/2007] (2007). http://mortality.org
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Špirková, J., Kollár, I., Szűcs, G., Zimmermann, P. (2023). Model of Longevity. In: Selected Payout Products of the Old-Age Pension Saving Scheme. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-23849-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-23849-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-23848-2
Online ISBN: 978-3-031-23849-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)