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Modeling trend processes in parametric mortality models

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  • Börger, Matthias
  • Schupp, Johannes

Abstract

Parametric mortality models like those of Lee and Carter (1992), Cairns et al. (2006), or Plat (2009) typically include one or more time dependent parameters. Often, a random walk with drift is used to project these parameters into the future. However, longer time series of historical mortality data often show patterns which a random walk with drift is highly unlikely to generate. In fact, historical mortality trends often appear to be trend stationary around piecewise linear trends with changing slopes over time (see, e.g., Sweeting (2011) or Li et al. (2011)). Periods of lower (but rather constant) mortality improvements are followed by periods of higher improvements and vice versa.

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  • Börger, Matthias & Schupp, Johannes, 2018. "Modeling trend processes in parametric mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 369-380.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:369-380
    DOI: 10.1016/j.insmatheco.2017.09.024
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    1. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    2. Hainaut, Donatien, 2012. "Multidimensional Lee–Carter model with switching mortality processes," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 236-246.
    3. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    4. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(4), pages 995-1029, August.
    5. Richards, S. J. & Currie, I. D. & Ritchie, G. P., 2014. "A Value-at-Risk framework for longevity trend risk," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 116-139, March.
    6. Cavaliere, Giuseppe & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2011. "Testing For Unit Roots In The Presence Of A Possible Break In Trend And Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 27(5), pages 957-991, October.
    7. Richards, Stephen, 2014. "A Value-at-Risk framework for longevity trend risk †Abstract of the London discussion," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 157-167, March.
    8. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    9. Andreas Milidonis & Yijia Lin & Samuel Cox, 2011. "Mortality Regimes and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 266-289.
    10. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    11. Edviges Coelho & Luis C. Nunes, 2011. "Forecasting mortality in the event of a structural change," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(3), pages 713-736, July.
    12. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    13. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    14. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Testing For A Unit Root In The Presence Of A Possible Break In Trend," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1545-1588, December.
    15. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    16. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    17. Börger, Matthias & Fleischer, Daniel & Kuksin, Nikita, 2014. "Modeling The Mortality Trend Under Modern Solvency Regimes," ASTIN Bulletin, Cambridge University Press, vol. 44(1), pages 1-38, January.
    18. Andrew Hunt & David Blake, 2014. "A General Procedure for Constructing Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 116-138.
    19. Wai-Sum Chan & Johnny Li & Jackie Li, 2014. "The CBD Mortality Indexes: Modeling and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 38-58.
    20. Jarner, Søren Fiig & Kryger, Esben Masotti, 2011. "Modelling Adult Mortality in Small Populations: The Saint Model," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 377-418, November.
    21. Sweeting, P. J., 2011. "A Trend-Change Extension of the Cairns-Blake-Dowd Model," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 143-162, September.
    22. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    23. Richards, Stephen, 2014. "A Value-at-Risk framework for longevity trend risk †Abstract of the Edinburgh discussion," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 140-156, March.
    24. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    25. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
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    Cited by:

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    3. Njenga, Carolyn Ndigwako & Sherris, Michael, 2020. "Modeling mortality with a Bayesian vector autoregression," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 40-57.
    4. Börger, Matthias & Freimann, Arne & Ruß, Jochen, 2021. "A combined analysis of hedge effectiveness and capital efficiency in longevity hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 309-326.

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    More about this item

    Keywords

    Longevity risk; Mortality projection; Parametric mortality models; Mortality trend process; Parameter uncertainty;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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