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Applying Survival Models to Pensioner Mortality Data

Published online by Cambridge University Press:  10 June 2011

S. J. Richards
S. J. Richards
Affiliation:
4 Caledonian Place, Edinburgh EH11 2AS, U.K.. Tel: +44 (0)131 315 4470; Email: [email protected] Web: www.richardsconsulting.co.uk
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Abstract

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.

Keywords

PostcodeZip CodeGeodemographic ModelsSurvival ModelsMortality LawsFrailtyAgeingReliability TheoryLate-Life Mortality DecelerationConcentration Risk
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 14 , Issue 2 , 01 July 2008 , pp. 257 - 303
Copyright
Copyright © Institute and Faculty of Actuaries 2008

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References

Aitken, M, Anderson, D, Francis, B. & Hinde, J. (1989). Statistical modelling in GLIM. Oxford University Press, 283–285.Google Scholar
Akaike, H. (1987). Factor analysis and AIC. Psychometrica, 52, 317–333.CrossRefGoogle Scholar
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, 302–311.Google Scholar
Boole, G. & Moulton, J.F. (1960). A treatise on the calculus of finite differences, 2nd revised edition. New York, Dover.Google Scholar
CACI Ltd (2007). http://www.caci.co.ukGoogle Scholar
Cox, D.R. (1972). Regression models and life tables. Journal of the Royal Statistical Society, Series B, 24, 187–220 (with discussion).Google Scholar
Cramer, H. (1999). Mathematical methods of statistics. Princeton University Press, ISBN13: 978-0-691-00547-8.Google Scholar
Currie, I.D., Durban, M. & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279–298.Google Scholar
Dickson, D.C.M. & Waters, H. R (2002). The distribution of the time to ruin in the classical risk model. ASTIN Bulletin, 32(2), 299–313.CrossRefGoogle Scholar
EuroDirect Database Marketing Ltd (2007). http://www.eurodirect.co.ukGoogle Scholar
Experian Ltd (2007). http://www.experianim.comGoogle Scholar
Gavrilov, L.A. & Gavrilova, N.S. (2001). The reliability theory of aging and longevity. Journal of Theoretical Biology, 213, 527–545.CrossRefGoogle ScholarPubMed
Gompertz, B. (1825). The nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society, 115, 513–585.Google Scholar
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), 245–267.CrossRefGoogle ScholarPubMed
Izsak, J. & Gavrilov, L.A. (1995). A typical interdisciplinary topic: questions of the mortality dynamics. Archives of Gerontology and Geriatrics, 20, 283–293.Google Scholar
Larson, H.J. (1982). Introduction to probability theory and statistical inference. John Wiley and Sons, Inc, New York, 318–319.Google Scholar
Legal and General plc (2007). Legal and General links with Hargreaves Lansdown to pioneer postcode-rated annuities. www.legalandgeneralmediacentre.comGoogle Scholar
Longevitas Development Team (2007). Longevitas v2.2. Longevitas Ltd, Edinburgh. http://www.longevitas.co.ukGoogle Scholar
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, 129–155.Google Scholar
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, 429–448.Google Scholar
Macdonald, A.S. (1996c). An actuarial survey of statistical models for decrement and transition data, III: counting process models. British Actuarial Journal, 2, 703–726.Google Scholar
Makeham, W.M. (1859). On the law of mortality and the construction of annuity tables. Journal of the Institute of Actuaries, 8, 301–310.Google Scholar
McCullagh, P. & Nelder, J.A. (1989). Generalized linear models, 2nd edn. Chapman and Hall, London.CrossRefGoogle Scholar
McLoone, P. (2000). Carstairs scores for Scottish postcode sectors from the 1991 census. Public Health Research Unit, University of Glasgow.Google Scholar
Park, S.K. & Miller, K.W. (1988). Communications of the ACM. Col. 31, 1192–1201.Google Scholar
Perks, W. (1932). On some experiments in the graduation of mortality statistics. Journal of the Institute of Actuaries, 63, 12–40.CrossRefGoogle Scholar
Philips, L. (1990). Hanging on the metaphone. Computer Language, 7(12), 39–43.Google Scholar
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.Google Scholar
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, http://www.r-project.orgGoogle Scholar
Richards, S.J. (2008). Detecting year-of-birth mortality patterns with limited data. Journal of the Royal Statistical Society, Series A, 171, Part 1, 279–298.Google Scholar
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, 1–18.CrossRefGoogle Scholar
Richards, S.J. & Jones, G.L. (2004). Financial aspects of longevity risk. Paper presented to the Staple Inn Actuarial Society.Google Scholar
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, 5–61.CrossRefGoogle Scholar
Strehler, B.L. & Mildvan, A.S. (1960). General theory of mortality and aging. Science 1, July, 14–21.Google Scholar
Vaupel, J.W. & Yashin, A.I. (1985). Heterogeneity's ruses: some surprising effects of selection on population dynamics. The American Statistician, 39(3), 176–185.CrossRefGoogle ScholarPubMed
Willets, R.C. (2004). The cohort effect: insights and explanations, British Actuarial Journal, 10, 833–898.CrossRefGoogle Scholar