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An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation

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  • Lin, Tzuling
  • Tzeng, Larry Y.
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    Abstract

    The paper proposes an additive continuous-time stochastic mortality model which revises that (B&H model) of Ballotta and Haberman (2006). The structure of the B&H model implies that the future hazard rate is proportional to the stochastic component, thus inducing two questionable features. First, in the B&H model, the uncertainty of the future hazard rate will be enlarged as the base hazard rate increases. However, an increase in the base hazard rate may not cause a dramatic increase suggested by the exponential component of B&H (2006). Second, in the B&H model, the uncertainty of the future hazard rate will be larger in the group which is older and will be greatly augmented by the interaction of age and time. But the uncertainty of the future hazard rate may not increase with an increase in age. The problems can be resolved by our additive structure which is the sum of a deterministic estimator and a stochastic component. Since using the additive structure will contribute to the fact that the stochastic component is independent of age and the base hazard rate, in our model the uncertainty of the future hazard rate will not be affected by an increase in age or in the base hazard rate. We further demonstrate an application of our model by calculating reserves of longevity risks for pure endowments and various common annuity products in the UK. We also compare our results with those of the B&H model.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 2 (April)
    Pages: 423-435

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    Handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:423-435

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Stochastic mortality Longevity risks Mortality risk Reserves Annuity;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 73(4), pages 647-672.
    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, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
    3. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David, 2006. "Mortality-dependent financial risk measures," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 38(3), pages 427-440, June.
    4. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(3), pages 299-318, December.
    5. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(2), pages 505-519, April.
    6. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 38(1), pages 195-214, February.
    7. Kevin Dowd & David Blake & Andrew J. G. Cairns & Paul Dawson, 2006. "Survivor Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 73(1), pages 1-17.
    8. da Rocha Neves, Cesar & Migon, Helio S., 2007. "Bayesian graduation of mortality rates: An application to reserve evaluation," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 40(3), pages 424-434, May.
    9. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 35(1), pages 113-136, August.
    10. Blake, David & Dowd, Kevin & Cairns, Andrew J.G., 2008. "Longevity risk and the Grim Reaper's toxic tail: The survivor fan charts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(3), pages 1062-1066, June.
    11. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(3), pages 443-468, December.
    12. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 38(1), pages 81-97, February.
    13. Hainaut, Donatien & Devolder, Pierre, 2008. "Mortality modelling with Lévy processes," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(1), pages 409-418, February.
    14. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 72(2), pages 227-252.
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    Cited by:
    1. Huang, Rachel J. & Miao, Jerry C.Y. & Tzeng, Larry Y., 2013. "Does mortality improvement increase equity risk premiums? A risk perception perspective," Journal of Empirical Finance, Elsevier, Elsevier, vol. 22(C), pages 67-77.

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