Skip to main content

Applying Survival Models to Pensioner Mortality Data

  • S. J. Richards (a1)

Data from insurance portfolios and pension schemes lend themselves particularly well to the application of survival models. In addition to the traditional actuarial risk-rating factors of age, gender and policy size, we find that using geodemographic models based on postcode provides a major boost in explaining risk variation. Geodemographic models can be better than models based on pension size in explaining socio-economic variation, but a model using both is usually better still. Models acknowledging heterogeneity tend to fit better than models which do not. Finally, bootstrapping techniques can be used to test the financial applicability of a model, while weighting the model fit can be used to address concentration risk.

Hide All
Aitken, M, Anderson, D, Francis, B. & Hinde, J. (1989). Statistical modelling in GLIM. Oxford University Press, 283285.
Akaike, H. (1987). Factor analysis and AIC. Psychometrica, 52, 317333.
Beard, R.E. (1959). Note on some mathematical mortality models. In: Wolstenholme, G.E.W. & O'Connor, M. (eds.). The Lifespan of Animals. Little, Brown, Boston, 302311.
Boole, G. & Moulton, J.F. (1960). A treatise on the calculus of finite differences, 2nd revised edition. New York, Dover.
CACI Ltd (2007).
Cox, D.R. (1972). Regression models and life tables. Journal of the Royal Statistical Society, Series B, 24, 187220 (with discussion).
Cramer, H. (1999). Mathematical methods of statistics. Princeton University Press, ISBN13: 978-0-691-00547-8.
Currie, I.D., Durban, M. & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279298.
Dickson, D.C.M. & Waters, H. R (2002). The distribution of the time to ruin in the classical risk model. ASTIN Bulletin, 32(2), 299313.
EuroDirect Database Marketing Ltd (2007).
Experian Ltd (2007).
Gavrilov, L.A. & Gavrilova, N.S. (2001). The reliability theory of aging and longevity. Journal of Theoretical Biology, 213, 527545.
Gompertz, B. (1825). The nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society, 115, 513585.
Horiuchi, S. & Coale, A.J. (1990). Age patterns of mortality for older women: an analysis using the age-specific rate of mortality change with age. Mathematical Population Studies, 2(4), 245267.
Izsak, J. & Gavrilov, L.A. (1995). A typical interdisciplinary topic: questions of the mortality dynamics. Archives of Gerontology and Geriatrics, 20, 283293.
Larson, H.J. (1982). Introduction to probability theory and statistical inference. John Wiley and Sons, Inc, New York, 318319.
Legal and General plc (2007). Legal and General links with Hargreaves Lansdown to pioneer postcode-rated annuities.
Longevitas Development Team (2007). Longevitas v2.2. Longevitas Ltd, Edinburgh.
Macdonald, A.S. (1996a). An actuarial survey of statistical models for decrement and transition data, I: multiple state, Poisson and Binomial models. British Actuarial Journal, 2, 129155.
Macdonald, A.S. (1996b). An actuarial survey of statistical models for decrement and transition data, II: competing risks, non-parametric and regression models. British Actuarial Journal, 2, 429448.
Macdonald, A.S. (1996c). An actuarial survey of statistical models for decrement and transition data, III: counting process models. British Actuarial Journal, 2, 703726.
Makeham, W.M. (1859). On the law of mortality and the construction of annuity tables. Journal of the Institute of Actuaries, 8, 301310.
McCullagh, P. & Nelder, J.A. (1989). Generalized linear models, 2nd edn. Chapman and Hall, London.
McLoone, P. (2000). Carstairs scores for Scottish postcode sectors from the 1991 census. Public Health Research Unit, University of Glasgow.
Park, S.K. & Miller, K.W. (1988). Communications of the ACM. Col. 31, 11921201.
Perks, W. (1932). On some experiments in the graduation of mortality statistics. Journal of the Institute of Actuaries, 63, 1240.
Philips, L. (1990). Hanging on the metaphone. Computer Language, 7(12), 3943.
Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. (2002). Numerical recipes in C++: the art of scientific computing. Cambridge University Press.
R Development Core Team (2004). R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0,
Richards, S.J. (2008). Detecting year-of-birth mortality patterns with limited data. Journal of the Royal Statistical Society, Series A, 171, Part 1, 279298.
Richards, S.J., Ellam, J.R., Hubbard, J., Lu, J.L.C., Makin, S.J. & Miller, K.A. (2007). Two-dimensional mortality data: patterns and projections, British Actuarial Journal, 14, 118.
Richards, S.J. & Jones, G.L. (2004). Financial aspects of longevity risk. Paper presented to the Staple Inn Actuarial Society.
Richards, S.J., Kirkby, J.G. & Currie, I.D. (2006). The importance of year of birth in two-dimensional mortality data. British Actuarial Journal, 12, 561.
Strehler, B.L. & Mildvan, A.S. (1960). General theory of mortality and aging. Science 1, July, 1421.
Vaupel, J.W. & Yashin, A.I. (1985). Heterogeneity's ruses: some surprising effects of selection on population dynamics. The American Statistician, 39(3), 176185.
Willets, R.C. (2004). The cohort effect: insights and explanations, British Actuarial Journal, 10, 833898.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

British Actuarial Journal
  • ISSN: 1357-3217
  • EISSN: 2044-0456
  • URL: /core/journals/british-actuarial-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed