A Poisson log-bilinear regression approach to the construction of projected lifetables. (English) Zbl 1074.62524
Summary: This paper implements Wilmoth’s [Computational methods for fitting and extrapolating the Lee–Carter model of mortality change, Technical report, Department of Demography, University of California, Berkeley] and Alho’s [North American Actuarial Journal 4, 91 (2000)] recommendation for improving the Lee–Carter approach to the forecasting of demographic components. Specifically, the original method is embedded in a Poisson regression model, which is perfectly suited for age–sex-specific mortality rates. This model is fitted for each sex to a set of age-specific Belgian death rates. A time-varying index of mortality is forecasted in an ARIMA framework. These forecasts are used to generate projected age-specific mortality rates, life expectancies and life annuities net single premiums. Finally, a Brass-type relational model is proposed to adapt the projections to the annuitants population, allowing for estimating the cost of adverse selection in the Belgian whole life annuity market.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62M20 | Inference from stochastic processes and prediction |
| 91D20 | Mathematical geography and demography |
Keywords:
Life insurance; Age–sex-specific mortality; Lifetable functions; Annuities; Adverse selectionSoftware:
LEMReferences:
| [1] | Alho, J. M., Discussion of Lee (2000), North American Actuarial Journal, 4, 91-93 (2000) |
| [2] | Benjamin, B., Soliman, A.S., 1993. Mortality on the Move. Institute of Actuaries, Oxford.; Benjamin, B., Soliman, A.S., 1993. Mortality on the Move. Institute of Actuaries, Oxford. |
| [3] | Brillinger, D. R., The natural variability of vital rates and associated statistics, Biometrics, 42, 693-734 (1986) · Zbl 0611.62136 |
| [4] | Brouhns, N., Denuit, M., 2001a. Risque de longévité et rentes viagères. I. Evolution de la mortalité en Belgique de 1880 nos jours. Discussion Paper. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique.; Brouhns, N., Denuit, M., 2001a. Risque de longévité et rentes viagères. I. Evolution de la mortalité en Belgique de 1880 nos jours. Discussion Paper. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique. |
| [5] | Brouhns, N., Denuit, M., 2001b. Risque de longévité et rentes viagères. II. Tables de mortalité prospectives pour la population belge. Discussion Paper. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique.; Brouhns, N., Denuit, M., 2001b. Risque de longévité et rentes viagères. II. Tables de mortalité prospectives pour la population belge. Discussion Paper. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique. |
| [6] | Brouhns, N., Denuit, M., 2001c. Risque de longévité et rentes viagères. III. Elaboration de tables de mortalité prospectives pour la population assurée belge, et évaluation du coût de l’antisélection. Discussion Paper. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique.; Brouhns, N., Denuit, M., 2001c. Risque de longévité et rentes viagères. III. Elaboration de tables de mortalité prospectives pour la population assurée belge, et évaluation du coût de l’antisélection. Discussion Paper. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique. |
| [7] | Brouhns, N., Denuit, M., Vermunt, J.K., 2002. Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries.; Brouhns, N., Denuit, M., Vermunt, J.K., 2002. Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries. · Zbl 1187.62158 |
| [8] | Carter, L. R.; Lee, R. D., Modeling and forecasting US sex differentials in mortality, International Journal of Forecasting, 8, 393-411 (1992) |
| [9] | Coppola, M.; Di Lorenzo, E.; Sibillo, M., Risk sources in a life annuity portfolio: decomposition and measurement tools, Journal of Actuarial Practice, 8, 43-61 (2000) · Zbl 1066.91564 |
| [10] | Cramér, H.; Wold, H., Mortality variations in Sweden: a study in graduation and forecasting, Scandinavian Actuarial Journal, 18, 161-241 (1935) · Zbl 0012.36306 |
| [11] | Goodman, L. A., Simple models for the analysis of association in cross-classifications having ordered categories, Journal of the American Statistical Association, 74, 537-552 (1979) |
| [12] | Gutterman, S.; Vanderhoof, I. T., Forecasting changes in mortality: a search for a law of causes and effects, North American Actuarial Journal, 2, 135-138 (2000) · Zbl 1081.91602 |
| [13] | Lee, R. D., The Lee-Carter method of forecasting mortality, with various extensions and applications, North American Actuarial Journal, 4, 80-93 (2000) · Zbl 1083.62535 |
| [14] | Lee, R. D.; Carter, L., Modelling and forecasting the time series of US mortality, Journal of the American Statistical Association, 87, 659-671 (1992) |
| [15] | Lee, R.D., Nault, F., 1993. Modeling and forecasting provincial mortality in Canada. Paper presented at the World Congress of International Union for the Scientific Study of Population, Montre’al.; Lee, R.D., Nault, F., 1993. Modeling and forecasting provincial mortality in Canada. Paper presented at the World Congress of International Union for the Scientific Study of Population, Montre’al. |
| [16] | Lee, R.D., Rofman, R., 1994. Modelacion y proyeccion de la mortalidad in Chile. Natas 22 (59), 182-313 (available in English from the authors, titled “Modeling and forecasting mortality in Chile”).; Lee, R.D., Rofman, R., 1994. Modelacion y proyeccion de la mortalidad in Chile. Natas 22 (59), 182-313 (available in English from the authors, titled “Modeling and forecasting mortality in Chile”). |
| [17] | Marocco, P., Pitacco, E., 1998. Longevity risk and life annuity reinsurance. In: Transactions of the 26th International Congress of Actuaries, Birmingham, pp. 453-479.; Marocco, P., Pitacco, E., 1998. Longevity risk and life annuity reinsurance. In: Transactions of the 26th International Congress of Actuaries, Birmingham, pp. 453-479. |
| [18] | McDonald, A. S., An actuarial survey of statistical models for decrement and transition data. I. Multiple state, Poisson and binomial models, British Actuarial Journal, 2, 129-155 (1996) |
| [19] | McDonald, A. S., 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 (1996) |
| [20] | McDonald, A. S., An actuarial survey of statistical models for decrement and transition data. III. Counting process model, British Actuarial Journal, 2, 703-726 (1996) |
| [21] | Olivieri, A., Uncertainty in mortality projections: an actuarial perspective, Insurance: Mathematics and Economics, 29, 231-245 (2001) · Zbl 0989.62058 |
| [22] | Olivieri, A., Pitacco, E., 1999. Funding sickness benefits for the elderly. In: Proceedings of the 30th ASTIN Colloquium, Tokyo, pp. 135-155.; Olivieri, A., Pitacco, E., 1999. Funding sickness benefits for the elderly. In: Proceedings of the 30th ASTIN Colloquium, Tokyo, pp. 135-155. |
| [23] | Olivieri, A., Pitacco, E., 2000. Solvency requirements for life annuities. In: Proceedings of the AFIR 2000 Colloquium, Tromso, Norway, pp. 547-571.; Olivieri, A., Pitacco, E., 2000. Solvency requirements for life annuities. In: Proceedings of the AFIR 2000 Colloquium, Tromso, Norway, pp. 547-571. |
| [24] | Olivieri, A., Pitacco, E., 2001. Facing LTC risks. Paper presented at the International Congress on Insurance: Mathematics and Economics, Penn State.; Olivieri, A., Pitacco, E., 2001. Facing LTC risks. Paper presented at the International Congress on Insurance: Mathematics and Economics, Penn State. |
| [25] | Renshaw, A. E.; Haberman, S., The modelling of recent mortality trends in the United Kingdom male assured lives, British Actuarial Journal, 2, 449-477 (1996) |
| [26] | Renshaw, A.E., Haberman, S., 2002. Lee-Carter mortality forecasting with age specific enhancement. Paper presented at the International Conference on Insurance: Mathematics and Economics, Lisbon, July 2002.; Renshaw, A.E., Haberman, S., 2002. Lee-Carter mortality forecasting with age specific enhancement. Paper presented at the International Conference on Insurance: Mathematics and Economics, Lisbon, July 2002. · Zbl 1103.91371 |
| [27] | Sithole, T. Z.; Haberman, S.; Verrall, R. J., An investigation into parametric models for mortality projections, with applications to immediate annuitants and life office pensioners’ data, Insurance: Mathematics and Economics, 27, 285-312 (2000) · Zbl 1055.62555 |
| [28] | Tuljapurkar, S.; Boe, C., Mortality change and forecasting: how much and how little do we know, North American Actuarial Journal, 2, 13-47 (1998) · Zbl 1081.91603 |
| [29] | Vermunt, J.K., 1997a. Log-linear Models for Event Histories. Sage, Thousand Oakes.; Vermunt, J.K., 1997a. Log-linear Models for Event Histories. Sage, Thousand Oakes. |
| [30] | Vermunt, J.K., 1997b. LEM: A General Program for the Analysis of Categorical Data. Users’ manual. Tilburg University, Tilburg, The Netherlands. http://www.kub.nl/mto; Vermunt, J.K., 1997b. LEM: A General Program for the Analysis of Categorical Data. Users’ manual. Tilburg University, Tilburg, The Netherlands. http://www.kub.nl/mto |
| [31] | Wilmoth, J.R., 1993. Computational methods for fitting and extrapolating the Lee-Carter model of mortality change. Technical report. Department of Demography. University of California, Berkeley.; Wilmoth, J.R., 1993. Computational methods for fitting and extrapolating the Lee-Carter model of mortality change. Technical report. Department of Demography. University of California, Berkeley. |
| [32] | Wilmoth, J.R., 1996. Mortality projections for Japan: a comparison of four methods. In Caselli, G., Lopez, A. (Eds.), Health and Mortality among Elderly Populations. Oxford University Press, New York, pp. 266-287.; Wilmoth, J.R., 1996. Mortality projections for Japan: a comparison of four methods. In Caselli, G., Lopez, A. (Eds.), Health and Mortality among Elderly Populations. Oxford University Press, New York, pp. 266-287. |
| [33] | Wilmoth, J.R., 1997. In search of limits. In: Between Zeus and the Salmon: The Biodemography of Longevity. National Academy of Science, pp. 38-64.; Wilmoth, J.R., 1997. In search of limits. In: Between Zeus and the Salmon: The Biodemography of Longevity. National Academy of Science, pp. 38-64. |
| [34] | Wilmoth, J. R., Demography of longevity: past, present and future trends, Experimental Gerontology, 35, 1111-1129 (2000) |
| [35] | Wilmoth, J. R.; Deegan, L. J.; Lundström, H.; Horiuchi, S., Increase of maximum life-span in Sweden, 1861-1999, Science, 289, 2366-2369 (2000) |
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