Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-14T15:14:40.159Z Has data issue: false hasContentIssue false
  • English
  • Français

Longevity in the 21st Century

Published online by Cambridge University Press:  10 June 2011

R. C. Willets ,
A. P. Gallop ,
P. A. Leandro ,
J. L. C. Lu ,
A. S. Macdonald ,
K. A. Miller ,
S. J. Richards ,
N. Robjohns ,
J. P. Ryan  and
H. R. Waters
R. C. Willets
Affiliation:
Willets Consulting, 1 Crealock Grove, Woodford Green, Essex IG8 9QZ, U.K., Tel: +44(0)208-505-9006, Email: richard@willets.co.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The main objective of this paper is to offer a detailed analysis of mortality change in the United Kingdom at the beginning the 21st century. Starting from an exploration of 20th century mortality trends, focusing in particular on the 1990s, underlying forces driving trends in longevity are discussed. These include the ‘cohort effect’ and the ‘ageing of mortality improvement’. International mortality statistics and trends are also analysed. The pace of medical advances is discussed, with specific focus on research into the ageing process and a potential treatment for cardiovascular disease. The paper also discusses the potential threat from infectious diseases.

The analysis of underlying trends suggests that life expectancy in retirement in the U.K. is likely to increase rapidly in the early part of the 21st century. Some scientists are also claiming that we will be seeing the fruits of anti-ageing research within just a few decades.

A core theme of the paper is that future projections should be grounded in as good an understanding of the past as possible. Different methods for projecting future rates of mortality are discussed, and it is noted that emphasis should be placed on the uncertainty surrounding projections.

The financial impact of using different assumptions for future mortality is explored. Significant differences in the cost of an annuity or pension arise from the use of the various projection bases.

Life assurance companies have already declared significant losses as a result of strengthening reserves on annuity portfolios. Taken together, future increases in life expectancy, increasing awareness of the risk of providing longevity insurance, changes in legislation and shortages in market capacity and capital, may well lead to worsening annuity rates.

It is difficult to assess the precise impact of future changes in life expectancy on final salary pension schemes. There is a lack of readily available information on the mortality assumptions being used in practice. It is therefore suggested that more disclosure in this area would be helpful. Employers sponsoring final salary schemes are making promises to their employees that extend up to 70 or 80 years into the future. Actuaries should be clear in spelling out to employers and trustees the nature of the risks behind the promises they are making. Future scheme design should reflect the possibility of substantial increases in life expectancy.

An over-riding implication of the anticipated increases in life expectancy is that people will remain in work for longer in the future. The age at which people retire will inevitably have to increase, and this trend will necessarily drive changes in all aspects of our society. As actuaries we have a vital role in helping to inform the wider debate.

Keywords

MortalityLongevityAgeingAnnuitiesCohort Effect
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 10 , Issue 4 , 01 October 2004 , pp. 685 - 832
Copyright
Copyright © Institute and Faculty of Actuaries 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ainslie, R. (2000). Annuity and insurance products for impaired lives. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Austad, S.N. (1997). Why we age. John Wiley & Sons, New York.Google Scholar
Beeching, N.J., Dance, D.A.B., Miller, A.R.O. & Spencer, R.C. (2002). Biological warfare and bioterrorism. British Medical Journal, 324, 336–339.Google Scholar
Benjamin, B. (1982). The span of life. Journal of the Institute of Actuaries, 109, 319–357.Google Scholar
Benjamin, B. & Soliman, A.S. (1993). Mortality on the move: methods of mortality projection. City University.Google Scholar
Bird, S.M., Goldberg, D.J. & Hutchinson, S.J. (2001a). Projecting severe sequelae of injection-related hepatitis C virus epidemic in the U.K. - Part 1. Journal of Epidemiology andBiostatistics, 6, 3, 243–265.Google Scholar
Bird, S.M., Goldberg, D.J. & Hutchinson, S.J. (2001b). Projecting severe sequelae of injection-related hepatitis C virus epidemic in the U.K. - Part 2. Journal of Epidemiology and Biostatistics. 6, 3, 267–277.Google Scholar
Bodnar, A.G., Ouellette, M., Frolkis, M., Holt, S.E., Chiu, C.P., Morin, G.B., Harley, C.B., Shay, J.W., Lichtsteiner, S. & Wright, W.E. (1998). Extension of life-span by introduction of telomerase into normal human cells. Science, 279(5349), 349–352.Google Scholar
Boelle, P.Y., Thomas, G., Valleron, A.J., Cesbron, J.Y. & Will, R. (2003). Modelling the epidemic of variant Creutzfeldt-Jakob disease in the U.K. based on age characteristics: updated, detailed analysis. Statistical Methods in Medical Research, 12, 3, 221–233.CrossRefGoogle Scholar
Brackenridge, R.D.C. & Elder, W.J. (1998). Medical selection of life risks. Fourth edition. Macmillan Ltd.Google Scholar
B.B.C. News Online (2001). France's glamorous grannies battle time. BBC News, 27 July 2001. Available at http://news.bbc.co.uk/1/hi/programmes/from_our_own_correspondent/1460770.stmGoogle Scholar
B.B.C. News Online (2003a). Dolly the cloned sheep dies. BBC News, 14 February 2003. Available at http://news.bbc.co.uk/1/hi/sci/tech/2764363.stmGoogle Scholar
B.B.C. News Online (2003b). Secret of cancer's ‘eternal youth’. BBC News, 1 February 2003. Available at http://news.bbc.co.uk/1/hi/health/2709151.stmGoogle Scholar
B.B.C. News Online (2003c). Italians flock to pensions protest. BBC News, 6 December 2003. Available at http://news.bbc.co.uk/1/hi/world/europe/3296917.stmGoogle Scholar
British Heart Foundation (2003). Coronary heart disease statistics 2003. www.heartstats.orgGoogle Scholar
Caselli, G. (1996). Future longevity among the elderly. In Health and mortality among elderly populations. Edited by Caselli, Graziella and Lopez, Alan D.. Clarendon Press, Oxford.CrossRefGoogle Scholar
Center for Strategic and International Studies and Watson Wyatt Worldwide (2003). The 2003 aging vulnerabiliy index. www.csis.orgGoogle Scholar
CMI Bureau (1999). CMI report number 17. CMI Bureau.Google Scholar
CMI Bureau Mortality Sub-Committee (2002). Working paper 1: an interim basis for adjusting the ‘92 series’ mortality projections for cohort effects. CMI, London.Google Scholar
Cousens, S., Everington, D., Ward, H.J.T., Huillard, J., Will, R.G. & Smith, P.G. (2003). The geographical distribution of variant Creutzfeldt-Jakob disease cases in the U.K.: what can we learn from it? Statistical Methods in Medical Research, 12, 3, 235–246.Google Scholar
Critical Illness Trends Research Group (2003). Presentation to the 2003 Healthcare Conference, Warwick.Google Scholar
Crowcroft, N.S. & Catchpole, M. (2002). Mortality from methicillin resistant Staphylococcus aureus in England and Wales: analysis of death certificates. British MedicalJournal, 325, 1390–1391.Google Scholar
Cruijsen, H. & Ding, H. (2002). Latest national mortality forecasts in Europe. Presentation to the Eurostat working party on demographic projections 16-17 September 2002.Google Scholar
De Grey, A.D.N.J. (2003). The foreseeability of real anti-aging medicine: focusing the debate. Experimental Gerontology, 38, 927–934.CrossRefGoogle ScholarPubMed
Department of Health (1999). Saving lives: our healthier nation. H.M.S.O., London.Google Scholar
Department of Health (2003). Chief Executive's report to the NHS. Department of Health Publications, London.Google Scholar
Deuffic, S., Poynard, T. & Valleron, A.J. (1999). Correlation between hepatitis C virus prevalence and hepatocellular carcinoma mortality in Europe. Journal of Viral Hepatitis, 6, 5, 411–413.Google Scholar
Donkin, A., Goldblatt, P. & Lynch, K. (2002). Inequalities in life expectancy by social class, 1972-1999. Health Statistics Quarterly, 15, 5–15.Google Scholar
Doll, R., Peto, R., Wheatley, K., Gray, R. & Sutherland, I. (1994). Mortality in relation to smoking: 40 years' observations on male British doctors. British Medical Journal, 309, 901–911.CrossRefGoogle ScholarPubMed
Dormont, D. (2002). Prion diseases: pathogenesis and public concerns. F.E.B.S. letters, 529, 17–21.CrossRefGoogle Scholar
Drucker, P. (1999). Innovate or die. The Economist. 25/9/1999.Google Scholar
Eurocare Working Group (2003). Eurocare-3 summary: cancer survival in Europe at the end of the 20th century. Ann Oncol. 14, Suppl 5, 128–149.Google Scholar
Faculty of Actuaries and Institute of Actuaries Pensions Board (2000). Review of the Minimum Funding Requirement. A report to the Secretary of State for Social Security.Google Scholar
Faculty of Actuaries and Institute of Actuaries Pensions Board (2001). Review of the MFR basis. A letter to the Department of Work and Pensions.Google Scholar
Flynn, M.A., Weaver-Osterholtz, D., Sharpe-Timms, K.L., Allen, S. & Krause, G. (1999). Dehydroepiandrosterone replacement in aging humans. Journal of Clinical Endocrinology and Metabolism, 84, 1527–1533.Google Scholar
Franciscus, A. (2003). Considering HCV treatment? — Know your genotype and viral load. Hepatitis C Support Project — HCV Advocate June 2003. www.hcvadvocate.orgGoogle Scholar
Food Standards Agency (2002). F.S.A. consumer attitudes to food survey — 2001. www.food.gov.ukGoogle Scholar
Friedman, D.B. & Johnson, T.E. (1988). A mutation in the age-1 gene in caenorhabditis elegans lengthens life and reduces hermaphrodite fertility. Genetics, 118(1), 75–86.Google Scholar
Ghani, A.C., Ferguson, N.M., Donnelly, C.A. & Anderson, R.M. (2003). Factors determining the pattern of the variant Creutzfeldt-Jakob disease (vCJD) epidemic in the U.K. Proceedings: Biological Sciences, 270, 1516, 689–698.Google Scholar
Government Actuary's Department (1995). National population projections 1992-based. H.M.S.O., London.Google Scholar
Government Actuary's Department (2001). National population projections: review of methodology for projecting mortality. Government Actuary's Department, London.Google Scholar
Government Actuary's Department (2002). National population projections 2000-based. H.M.S.O., London.Google Scholar
Government Actuary's Department (2003a). Interim life tables 2000-02. www.gad.gov.ukGoogle Scholar
Government Actuary's Department (2003b). Government Actuary's quinquennial review of the National Insurance Fund as at April 2000. H.M.S.O.Google Scholar
Government Actuary's Department (2003c). ‘2002-based’ U.K. population projections. www.gad.gov.ukGoogle Scholar
Hahn, W.C., Counter, C.M., Lundberg, A.S., Beijersbergen, R.L., Brooks, M.W. & Weinberg, R.A. (1999). Creation of human tumour cells with defined genetic elements. Nature. 400(6743), 464–468.Google Scholar
Hawkes, N. (2003). £1 ‘superpill’ could cut heart attacks by 80%. The Times, June 27, 2003. Available at http://www.timesonline.co.uk/article/0%2c%2c2-727079%2c00.htmlGoogle Scholar
Hayflick, L. & Moorhead, P. (1961). The serial cultivation of human diploid cell strains. Experimental Cell Research, 25, 585–621.Google Scholar
Heath, P.T. & Breathnach, A.S. (2002). Treatment of infections due to resistant organisms. British MedicalJournal, 61, 231–245.Google Scholar
Held, G. (2002). Plastic omega. Paper presented to the Society of Actuaries symposium: ‘Living to 100 and beyond: survival at advance ages’.Google Scholar
Hewitt Bacon & Woodrow (2004). Pension scheme deficits halved as equity markets deliver positive returns for 2003. www.hewittbaconwoodrow.co.ukGoogle Scholar
HM Treasury/Inland Revenue (2003). Simplifying the taxation of pensions: the Government's proposals. H.M.S.O.Google Scholar
Horan, M. (1998). Advances in understanding the concept of biological ageing. In Increasing longevity: medical, social and political implications. Edited by Tallis, Raymond. Royal College of Physicians.Google Scholar
Housholder, J. (1998). From smokers to ex-smokers. The Cologne Re Risk Insights, Vol. 2, No. 3, 4–7.Google Scholar
Howitz, K.T., Bitterman, K.J., Cohen, H.Y., Lamming, D.W., Lavu, S., Wood, J.G., Zipkin, R.E., Chung, P., Kisielewski, A., Zhang, L.L., Scherer, B. & Sinclair, D.A. (2003). Small molecule activators of sirtuins extend saccharomyces cerevisiae lifespan. Nature, 425(6954), 191–196.CrossRefGoogle ScholarPubMed
Huillard D'Aignaux, J.N., Cousens, S.N. & Smith, P.G. (2003). The predictability of the epidemic of variant Creutzfeldt-Jakob disease by back-calculation methods. Statistical Methods in Medical Research, 12, 3, 203–220.Google Scholar
Human Mortality Database (2003). www.mortality.orgGoogle Scholar
JP Morgan (2003). U.K. insurance: annuities — the die is cast. JP Morgan European Equity Research, 30 October 2003.Google Scholar
Kaku, M. (1998). Visions: how science will revolutionize the 21st century. Bantam Books.Google Scholar
Kannisto, V. (1994). Development of oldest-old mortality, 1950-1990: Evidence from 28 developed countries. University Press of Southern Denmark.Google Scholar
Kirkwood, T.B.M. (1998). Genetics and the future of human longevity. In Increasing longevity: medical, social and political implications. Edited by Tallis, Raymond. Royal College of Physicians.Google Scholar
Kirkwood, T.B.L. (2004). Expectations of life. British Actuarial Journal, 10, 75–100.Google Scholar
La Vecchia, C., Lucchini, F., Franceschi, S., Negri, E. & Levi, F. (2000). Trends in mortality from primary liver cancer in Europe. European Journal of Cancer, 36, 7, 909–915.Google Scholar
Larkin, M. (1998). DHEA: will science confirm the headlines? The Lancet, 352(9123).Google Scholar
Law, M.R., Wald, N.J., Morris, J.K. & Jordan, R.E. (2003). Value of low dose combination treatment with blood pressure lowering drugs: analysis of 354 randomised trials. British Medical Journal, 326, 1427–1431.Google Scholar
Law, M.R., Wald, N.J. & Rudnicka, A.R. (2003). Quantifying the effect of statins on low density lipoprotein cholesterol, ischaemic heart disease, and stroke: systematic review and meta-analysis. British Medical Journal, 326, 1423–1427.CrossRefGoogle ScholarPubMed
Liddle, B.J. & Jennings, R. (2001). Influenza vaccination in old age. Age and Ageing, 30, 385–389.Google Scholar
Lucas, G.M. (2003). Taking HAART to heart: antiretroviral toxicity. The Hopkins HIV Report - March 2003.Google Scholar
Macdonald, A.S., Waters, H.R. & Wekwete, C.T. (2003). A model for coronary heart disease and stroke with applications to critical illness insurance underwriting I: The model. Submitted for publication. Available at http://www.ma.hw.ac.uk/ams.htmlGoogle Scholar
MacMinn, R. (2003). International mortality comparisons. Presentation to the Society of Actuaries, Vancouver. www.journalofriskandinsurance.orgGoogle Scholar
Marmot, M., Bosma, H., Hemingway, H., Brunner, E. & Stansfield, S. (1997). Contribution of job control and other risk factors to social variations in coronary heart disease incidence. The Lancet, 350, 235–239.Google Scholar
Marra, M.A., Jones, S.J.M., Astell, C.R.et al. (2003). The genome sequence of the SARS-associated coronavirus. Science, 300, 1399.Google Scholar
Medina, J. (1996). The clock of ages: why we age — how we age — winding back the clock. Cambridge University Press.Google Scholar
Morales, C.P., Holt, S.E., Ouelette, M., Kaur, K.J., Yan, Y., Wilson, K.S., White, M.A., Wright, W.E. & Shay, J.W. (1999). Absence of cancer-associated changes in human fibroblasts immortalized with telomerase. Nature Genetics, 21, 115–118.Google Scholar
Muir, D.S. & Griffin, G.E. (2001). Infection risks in xenotransplantation — prepared for the Department of Health. Department of Health. www.doh.gov/ukxira.htmGoogle Scholar
Myint, S.H., Kilvington, S., Maggs, A., Swann, R.A. & Norman, R.I. (1999). Principles of infectious disease. In Medical microbiology made memorable. Churchill Livingstone.Google Scholar
National Heart Forum (1999). Looking to the future: making coronary heart disease an epidemic of the past. The Stationery Office, London.Google Scholar
O'Brien, C. (2003). The challenge of increased longevity for pension providers. Paper presented to the 25th U.K. Insurance Economists' Conference. Nottingham University Business School.Google Scholar
Oeppen, J. & Vaupel, J. (2002). Broken limits to life expectancy. Science, 296, 1029–1031.CrossRefGoogle ScholarPubMed
Office of National Statistics (1997a). The health of adult Britain 1841-1994. H.M.S.O., London.Google Scholar
Office of National Statistics (1997b). Health inequalities. H.M.S.O., London.Google Scholar
Office of National Statistics (2002). Living in Britain: results from the 2001 General Household Survey. H.M.S.O., London.Google Scholar
Office of National Statistics (2003). Twentieth century mortality. H.M.S.O., London.Google Scholar
Olshansy, S.J., Hayflick, L. & Carnes, B.A. (2002). Position statement on human aging. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 57, B292–B297.CrossRefGoogle Scholar
Pawlotsky, J.M. (2003). Mechanisms of antiviral treatment efficacy and failure in chronic hepatitis C. Antiviral Research, 59, 1, 1–11.CrossRefGoogle ScholarPubMed
PHLS (2001). Antimicrobial resistance in 2000 in England and Wales.Google Scholar
PHLS (2003a). HIV infection and AIDS in the United Kingdom: monthly report - April 2003 (A survey of HIV infections diagnosed in 2002). CDR Weekly - 25 April 2003. 13, 17.Google Scholar
PHLS (2003b). HIV infection in women giving birth in the United Kingdom: trends in prevalence and proportions diagnosed to the end of June 2002. CDR Weekly - 27 March 2003. 13, 13.Google Scholar
PHLS (2003c). AIDS and HIV infection in the United Kingdom: monthly report - February 2003 (Analysis of end year HIV data: 2002). CDR Weekly - 20 February 2003. 13, 8.Google Scholar
PHLS (2003d). HIV and women in the U.K. CDR Weekly - 3 January 2003.Google Scholar
PHLS (2003e). Tuberculosis update March 2003.Google Scholar
Quinn, T.C. (2003). World AIDS day: reflection on the pandemic. The Hopkins HIV Report - January 2003.Google Scholar
Rodgers, A. (2003). A cure for cardiovascular disease? British Medical Journal, 326, 1407–1408.CrossRefGoogle ScholarPubMed
Rota, P.A., Oberste, M.S., Monroe, S.S.et al. (2003). Characterization of a novel corornavirus associated with severe acute respiratory syndrome. Science, 300, 1394–1399.Google Scholar
Roth, G.S., Lane, M.A., Ingram, D.K., Mattison, J.A., Elahi, D., Tobin, J.D., Muller, D. & Metter, E.J. (2002). Biomarkers of caloric restriction may predict longevity in humans. Science, 297, 811.Google Scholar
Rubin, H. (1998). Telomerase and cellular lifespan: ending the debate? Nat Biotechnol., 16(5), 396–397.CrossRefGoogle ScholarPubMed
Rudolph, K.L., Chang, S., Millard, M., Schreiber-Agus, N. & DePinho, R.A. (2000). Inhibition of experimental liver cirrhosis in mice by telomerase gene delivery. Science, 287(5456), 1253–1258.CrossRefGoogle ScholarPubMed
Shiels, P.G., Kind, A.J., Campbell, K.H., Waddington, D., Wilmot, I., Colman, A., & Schnieke, A.E. (1999). Analysis of telomere lengths in cloned sheep. Nature, 399(6734), 316–317.Google Scholar
Sikora, K. (1999). Cancer survival in Britain. British Medical Journal, 319, 461–462.CrossRefGoogle ScholarPubMed
Smith, R. (2003). The most important BMJ for 50 years? British Medical Journal, 326.Google Scholar
Spencer, R.C. (2002). Deaths from MRSA. British Medical Journal, Rapid release - 17 December 2002.Google Scholar
Sze, M. & Rosenberg, M. (1998). Overview: impact of mortality improvement on social security in Canada, Mexico and the United States. North American Actuarial Journal, Vol. 2, No. 4, 83–107.CrossRefGoogle Scholar
Szutorisz, H., Lingner, J., Cuthbert, A.P., Trott, D.A., Newbold, R.F. & Nabholz, M. (2003). A chromosome 3-encoded repressor of the human telomerase reverse transcriptase (hTERT) gene controls the state of hTERT chromatin. Cancer Res. 63(3), 689–695.Google Scholar
Tabeau, E. (2001). A review of demographic forecasting models for mortality. In Forecasting mortality in developed countries. Edited by Tabeau, Ewa, Jeths, Anneke van den Berg and Heathcote, Christopher. Kluwer Academic Publishers.Google Scholar
Terajima, T., Yamagata, S., Satoh, N. & Ueda, S. (2003). Meta-analysis: effect of ACE inhibitors on outcomes in patients with renal insufficiency. The Pharmacy and Therapeutics Journal. Available at http://216.119.117.233/ptjournal/fulltext/28/2/PTJ2802098.pdfGoogle Scholar
Thatcher, A.R. (1999). The demography of centenarians in England & Wales. Population Trends, 96, 5–10.Google Scholar
Todd, W.T.A. & Dundas, S. (2001). The management of VTEC O157 infection. International Journal of Food Microbiology, 66, 103–110.Google Scholar
Townsend, P. & Davidson, N. (1982). Inequalities in health: the Black report. Penguin Books.Google Scholar
Tuljapurkar, S. & Boe, C. (1998). Mortality change and forecasting: how much and how little do we know? North American Actuarial Journal, 2(4), 13–47.Google Scholar
Turner, A. (2003). The macro-economics of pensions. Lecture to the actuarial profession, 2 September 2003.Google Scholar
Turner, N.J., Howard, R.A., Mulley, G.P. & Selby, P.J. (1999). Cancer in old age: is it inadequately investigated and treated? British Medical Journal, 319, 309–312.Google Scholar
U.K. CJD Surveillance Unit (2003). CJD statistics - 4 July 2003. www.cjd.ed.ac.ukGoogle Scholar
UN AIDS & WHO (2002). AIDS epidemic update, December 2002. www.who.intGoogle Scholar
Valkonen, T. (2001). Trends in differential mortality in European countries. In Trends in mortality and differential mortality. Edited by Vallin, Jacques, Mesle, France & Valkonen, Tapani. Council of Europe Publishing, Strasbourg.Google Scholar
Vaupel, J. (1997). Trajectories of mortality at advanced ages. In Between Zeus and the salmon: the biodemography of longevity. Edited by Wachter, Kenneth and Finch, Caleb. National Academy Press, Washington.Google Scholar
Vellai, T., Takacs-Vellai, K., Zhang, Y., Kovacs, A.L., Orosz, L. & Muller, F. (2003). Influence of TOR kinase on lifespan in C. elegans. Nature, 426(6967), 620.Google Scholar
Wadsworth, M., Findlater, A. & Boardman, T. (2001). Reinventing annuities. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Wadsworth, M. (2003). The future of the pension annuity market. Association of British Insurers.Google Scholar
Wald, N.J. & Law, M.R. (2003). A strategy to reduce cardiovascular disease by more than 80%. British Medical Journal, 326, 1419–1423.Google Scholar
White, C. (2003). ‘Polypill’ to fight cardiovascular disease: summary of rapid responses. British Medical Journal, 327, 809.Google Scholar
WHO (2000). Weekly epidemiological record, 12, 75, 93–100. www.who.int/werGoogle Scholar
WHO (2002). Life tables for 191 countries. World mortality in 2000. www.who.intGoogle Scholar
WHO (2003). Severe acute respiratory syndrome (SARS): status of the outbreak and lessons for the immediate future. Geneva 20 May 2003.www.who.intGoogle Scholar
Wilkie, A.D., Waters, H.R. & Yang, S.Y. (2003). Reserving, pricing and hedging for policies with guaranteed annuity options. British Actuarial Journal, 9, 263–425 and 10, 101-152.CrossRefGoogle Scholar
Willets, R.C. (1999). Mortality in the next millennium. Paper presented to the Staple Inn Actuarial Society.Google Scholar
Willets, R.C. (2003). The cohort effect: insights & explanations. British Actuarial Journal, 10, 833–877.Google Scholar
Wilmot, J. & Lundstrom, H. (1996). Extreme longevity in five countries. European Journal of Population, 12(1). 63–93.Google Scholar
Wilmoth, J.R. (1997). In search of limits. In Between Zeus and the salmon: the biodemography of longevity. Edited by Wachter, Kenneth & Finch, Caleb. National Academy Press. Washington D.C.Google Scholar
Yerly, S., Kaiser, L., Race, E., Bru, J.P., Chavel, F. & Perrin, L. (1999). Transmission of antiretroviral-drug-resistant HIV-1 variants. The Lancet, 354, 729–733.Google Scholar