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A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. (English) Zbl 1484.91376

The paper analyses several stochastic models depicting improvements in mortality rates in England and Wales and in the United States. In particular, mortality improvements for males aged 60–89 are considered by means of eight stochastic mortality models that decompose mortality improvements into one or more age-, period-, and cohort-related effects. The Bayes information criterion allows to obtain that, for higher ages, an extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort effect fits the England and Wales males’ data best; moreover, the Renshaw and Haberman (RH) extension to the Lee and Carter model, that incorporates a cohort effect, provides the best fit of the U.S. males data. The study also explores some issues regarding the robustness of parameter estimates in the RH model, discussing its suitability for prediction; in addition, an extension to the CBD model that allows both a cohort effect and a quadratic age effect is investigated in terms of parameter stability.

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography
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[1] Anderson, R. N. 1999. Method for Constructing Complete Annual U.S. Life Tables. Vital and Health Statistics 2(129), National Center for Health Statistics.
[2] Blake, D. and Burrows, W. 2001. Survivor Bonds: Helping to Hedge Mortality Risk. Journal of Risk and Insurance, 68: 339-348.
[3] Blake, D., Cairns, A. J. G. and Dowd, K. 2006. Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities. British Actuarial Journal, 12: 153-97.
[4] Blake, D., Cairns, A. J. G., Dowd, K. and MaCMinn, R. 2006. Longevity Bonds: Financial Engineering, Valuation and Hedging. Journal of Risk and Insurance, 73: 647-72.
[5] Brouhns, N., Denuit, M. and Vermunt, J. K. 2002. A Poisson Log-Bilinear Regression Approach to the Construction of Projected Life Tables. Insurance: Mathematics and Economics, 31: 373-93. · Zbl 1074.62524
[6] Cairns, A. J. G. 2000. A Discussion of Parameter and Model Uncertainty in Insurance. Insurance: Mathematics and Economics, 27: 313-30. · Zbl 0971.62063
[7] Cairns, A. J. G., Blake, D. and Dowd, K. 2006a. Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk. ASTIN Bulletin, 36: 79-120. · Zbl 1162.91403
[8] Cairns, A. J. G., Blake, D. and Dowd, K. 2006b. A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration. Journal of Risk and Insurance, 73: 687-718.
[9] Cairns, A. J. G., Blake, D. and Dowd, K. 2008. Measurement, Modelling and Management of Mortality Risk: A Review. Scandinavian Actuarial Journal, 2-3: 79-113. · Zbl 1224.91048
[10] Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D. and Khalaf-Allah, M. 2008. “Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models”. In Working paper Heriot-Watt University, and Pensions Institute Discussion Paper PI-0801. · Zbl 1231.91179
[11] Continuous Mortality Investigation Bureau (CMI). 2005. “Projecting Future Mortality: Towards a Proposal for a Stochastic Methodology”. In Working paper 15
[12] Continuous Mortality Investigation Bureau (CMI). 2006. “Stochastic Projection Methodologies: Further Progress and P-Spline Model Features, Example Results and Implications”. In Working paper 20
[13] Continuous Mortality Investigation Bureau (CMI). 2007. “Stochastic Projection Methodologies: Lee-Carter Model Features, Example Results and Implications”. In Working paper 25
[14] Currie, I. D. 2006. Smoothing and Forecasting Mortality Rates with P-Splines. Paper given at the Institute of Actuaries, June 2006. http://www.ma.hw.ac.uk/ iain/research/talks.html
[15] Currie, I. D., Durban, M. and Eilers, P. H. C. 2004. Smoothing and Forecasting Mortality Rates. Statistical Modelling, 4: 279-98. · Zbl 1061.62171
[16] Czado, C., Delwarde, A. and Denuit, M. 2005. Bayesian Poisson Log-Linear Mortality Projections. Insurance: Mathematics and Economics, 36: 260-84. · Zbl 1110.62142
[17] Dahl, M., Melchior, M. and Møller, T. 2008. On Systematic Mortality Risk and Risk Minimisation with Survivor Swaps. Scandinavian Actuarial Journal, 2-3: 114-46. · Zbl 1224.91054
[18] Dahl, M. and Møller, T. 2006. Valuation and Hedging of Life Insurance Risks with Systematic Mortality Risk. Insurance: Mathematics and Economics, 39: 193-217. · Zbl 1201.91089
[19] Dawson, P., Blake, D., Cairns, A. J. G. and Dowd, K. 2007. Completing the Survivor Derivatives Market Pensions Institute Discussion Paper PI-0712.
[20] Dowd, K., Blake, D., Cairns, A. J. G., Coughlan, G. D., Epstein, D. and Khalaf-Allah, M. 2008a. Evaluating the Goodness of Fit of Stochastic Mortality Models Pensions Institute Discussion Paper PI-0802. · Zbl 1231.91179
[21] Dowd, K., Blake, D., Cairns, A. J. G., Coughlan, G. D., Epstein, D. and Khalaf-Allah, M. 2008b. Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of Multi-Period-Ahead Density Forecasts Pensions Institute Discussion Paper PI-0803.
[22] Dowd, K., Blake, D., Cairns, A. J. G. and Dawson, P. 2006. Survivor Swaps. Journal of Risk and Insurance, 73: 1-17.
[23] Dowd, K., Cairns, A. J. G. and Blake, D. 2006. Mortality-Dependent Financial Risk Measures. Insurance: Mathematics andEconomics, 38: 427-40. · Zbl 1168.91411
[24] Hayashi, F. 2000. Econometrics, Princeton: Princeton University Press.
[25] JaCobsen, R., Keiding, N. and Lynge, E. 2002. Long-Term Mortality Trends behind Low Life Expectancy of Danish Women. Journal of Epidemiology and Community Health, 56: 205-8.
[26] Koissi, M. C., Shapiro, A. F. and HÖgnäs, G. 2006. Evaluating and Extending the Lee-Carter Model for Mortality Forecasting: Bootstrap Confidence Intervals. Insurance: Mathematics and Economics, 38: 1-20. · Zbl 1098.62138
[27] Lee, R. D. and Carter, L. R. 1992. Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87: 659-75.
[28] Osmond, C. 1985. Using Age, Period and Cohort Models to Estimate Future Mortality Rates. International Journal of Epidemiology, 14: 124-29.
[29] Perks, W. 1932. On Some Experiments in the Graduation of Mortality Statistics. Journal of the Institute of Actuaries, 63: 12-57.
[30] Renshaw, A. E. and Haberman, S. 2003. Lee-Carter Mortality Forecasting with Age-Specific Enhancement. Insurance: Mathematics and Economics, 33: 255-72. · Zbl 1103.91371
[31] Renshaw, A. E. and Haberman, S. 2006. A Cohort-Based Extension to the Lee-Carter Model for Mortality Reduction Factors. Insurance: Mathematics and Economics, 38: 556-70. · Zbl 1168.91418
[32] Richards, S. J., Kirkby, J. G. and Currie, I. D. 2006. The Importance of Year of Birth in Two-Dimensional Mortality Data. British Actuarial Journal, 12: 5-38.
[33] Willets, R. C. 1999. Mortality in the Next Millennium Paper presented to the Staple Inn Actuarial Society.
[34] Willets, R. C. 2004. The Cohort Effect: Insights and Explanations. British Actuarial Journal, 10: 833-77.
[35] Wong-Fupuy, C. and Haberman, S. 2004. Projecting Mortality Trends: Recent Developments in the United Kingdom and the United States. North American Actuarial Journal, 8(1): 56-83. · Zbl 1085.62517
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