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Pension plan valuation and mortality projection: a case study with mortality data. (English) Zbl 1480.91195

Summary: It is now well documented that human mortality globally declined during the course of the twentieth century. These mortality improvements pose a challenge for pricing and reserving in life insurance and for the management of public pension regimes. Assuming a further continuation of the stable pace of mortality decline, a Poisson log-bilinear projection model is applied to population mortality data to forecast future death rates. Then a relational model embedded in a Poisson regression approach is used to merge a dynamic mortality table based on data of a large population (in this case the Canadian province of Quebec) to mortality data of a given pension plan (here the Régie des Rentes du Québec) to create another dynamic mortality table, which can be used to make any assessments on the total costs of the pension plan. We provide at the end numerical examples that illustrate the impact of mortality improvements on a pension plan.

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Benjamin, B. and Soliman, A. S. 1993. Mortality on the Move, Oxford: Institute of Actuaries.
[2] Brillinger, D. R. 1986. The Natural Variability of Vital Rates and Associated Statistics. Biometrics, 42: 693-734. · Zbl 0611.62136
[3] Brouhns, N., Denuit, M. and Van Keilegom, I. 2005. Bootstrapping the Poisson Log-Bilinear Model for Mortality Projection. Scandinavian Actuarial Journal, : 212-224. · Zbl 1092.91038
[4] Brouhns, N., Denuit, M. and Vermunt, J. 2002a. A Poisson Log-Bilinear Regression Approach to the Construction of Projected Lifetables. Insurance: Mathematics and Economics, 31: 373-393. · Zbl 1074.62524
[5] Brouhns, N., Denuit, M. and Vermunt, J. 2002b. Measuring the Longevity Risk in Mortality Projections. Bulletin of the Swiss Association of Actuaries, : 105-130. · Zbl 1187.62158
[6] Buettner, Thomas. 2002. Approaches and Experiences in Projecting Mortality Patterns for the Oldest-Old. North American Actuarial Journal, 6(3): 14-25. · Zbl 1084.62524
[7] Coale, A. and Guo, G. 1989. Revised Regional Model Life Tables at Very Low Levels of Mortality. Population Index, 55: 613-643.
[8] Coale, A. and Kisker, E. E. 1990. Defects in Data on Old Age Mortality in the United States: New Procedures for Calculating Approximately Accurate Mortality Schedules and Life Tables at the Highest Ages. Asian and Pacific Population Forum, 4: 1-31.
[9] Delwarde, A. and Denuit, M. 2005. Construction de tables de mortalité périodiques et prospectives, Paris: Collection Audit-Actuariat-Assurance, Economica.
[10] Denuit, M. and Goderniaux, A.-C. 2004. Closing and Projecting Lifetables Using Log-Linear Models, Louvain-la-Neuve, Belgium: Université Catholique de Louvain. Working Paper 04-04, Institut des Sciences Actuarielles
[11] Goodman, L. A. 1979. Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories. Journal of the American Statistical Association, 74: 537-552.
[12] Gutterman, Sam and Vanderhoof, Irwin T. 1998. Forecasting Changes in Mortality: A Search for a Law of Causes and Effects. North American Actuarial Journal, 2(4): 135-138. · Zbl 1081.91602
[13] Horiuchi, S. and Wilmoth, J. R. 1998. Deceleration in the Age Pattern of Mortality at Older Ages. Demography, 35: 391-412.
[14] Lee, Ronald D. 2000. The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications. North American Actuarial Journal, 4(1): 80-93. · Zbl 1083.62535
[15] Lee, R. D. and Carter, L. 1992. Modelling and Forecasting the Time Series of US Mortality. Journal of the American Statistical Association, 87: 659-671.
[16] Lindbergson. 2001. Mortality among the Elderly in Sweden 1988-97. Scandinavian Actuarial Journal, : 79-94. · Zbl 0973.62106
[17] Mcdonald, 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.
[18] Mcdonald, 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.
[19] Mcdonald, A. S. 1996c. An Actuarial Survey of Statistical Models for Decrement and Transition Data. III: Counting Process Model. British Actuarial Journal, 2: 703-726.
[20] Mcdonald, A. S., Cairns, A. J. C., Gwilt, P. L. and Miller, K. A. 1998. An International Comparison of Recent Trends in Mortality. British Actuarial Journal, 4: 3-141.
[21] Pitacco, E. 2004. Survival Models in a Dynamic Context: A Survey. Insurance: Mathematics and Economics, 35: 279-298. · Zbl 1079.91050
[22] Renshaw, A. E. and Haberman, S. 2003a. Lee-Carter Mortality Forecasting: A Parallel Generalized Linear Modelling Approach for England and Wales Mortality Projection. Applied Statistics, 52: 119-137. · Zbl 1111.62359
[23] Renshaw, A. E. and Haberman, S. 2003b. Lee-Carter Mortality Forecasting with Age Specific Enhancement. Insurance: Mathematics and Economics, 33: 255-272. · Zbl 1103.91371
[24] Thatcher, A. R. 1999. The Long-Term Pattern of Adult Mortality and the Highest Attained Age. Journal of the Royal Statistical Society—Series A, 162: 5-43.
[25] Thatcher, A. R., Kannisto, V. and Andreev, K. 2002. The Survivor Ratio Method for Estimating Numbers at High Ages. Demographic Research, 6: 1-18.
[26] Thatcher, A. R., Kannisto, V. and Vaupel, J. W. 1998. The Force of Mortality at Ages 80 to 120, Odense, Denmark: Odense University Press. Odense Monographs on Population Aging 5
[27] Tuljapurkar, Shripad and Boe, Carl. 1998. Mortality Change and Forecasting: How Much and How Little Do We Know. North American Actuarial Journal, 2(4): 13-47. · Zbl 1081.91603
[28] Wilmoth, J. R. 1997. Search of Limits. Between Zeus and the Salmon: The Biodemography of Longevity, : 38-64. National Academy of Science
[29] Wilmoth, J. R. 2000. Demography of Longevity: Past, Present and Future Trends. Experimental Gerontology, 35: 1111-1129.
[30] Wilmoth, J. R., Deegan, L. J., Lundström, H. and Horiuchi, S. 2000. Increase of Maximum Life-span in Sweden, 1861-1999. Science, 289: 2366-2369.
[31] Wong-Fupuy, Carlos and Haberman, Steven. 2004. Projecting Mortality Trends: Recent Developments in the United Kingdom and the United States. North American Actuarial Journal, 8(2): 56-83. · Zbl 1085.62517
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