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Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models

  • Yang, Sharon S.
  • Yue, Jack C.
  • Huang, Hong-Chih
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    This research proposes a mortality model with an age shift to project future mortality using principal component analysis (PCA). Comparisons of the proposed PCA model with the well-known models--the Lee-Carter model, the age-period-cohort model (Renshaw and Haberman, 2006), and the Cairns, Blake, and Dowd model--employ empirical studies of mortality data from six countries, two each from Asia, Europe, and North America. The mortality data come from the human mortality database and span the period 1970-2005. The proposed PCA model produces smaller prediction errors for almost all illustrated countries in its mean absolute percentage error. To demonstrate longevity risk in annuity pricing, we use the proposed PCA model to project future mortality rates and analyze the underestimated ratio of annuity price for whole life annuity and deferred whole life annuity product respectively. The effect of model risk on annuity pricing is also investigated by comparing the results from the proposed PCA model with those from the LC model. The findings can benefit actuaries in their efforts to deal with longevity risk in pricing and valuation.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4XG3S6V-1/2/ef57d6b532ef90a81a704f2915c194ba
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 1 (February)
    Pages: 254-270

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    Handle: RePEc:eee:insuma:v:46:y:2010:i:1:p:254-270
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Bauer, Daniel & Weber, Frederik, 2007. "Assessing Investment and Longevity Risks within Immediate Annuities," Discussion Papers in Business Administration 1982, University of Munich, Munich School of Management.
    2. 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.
    3. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    4. Pablo Antolín, 2007. "Longevity Risk and Private Pensions," OECD Working Papers on Insurance and Private Pensions 3, OECD Publishing.
    5. 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.
    6. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    7. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    8. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 505-519, April.
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