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Mortality risk modeling: Applications to insurance securitization

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  • Cox, Samuel H.
  • Lin, Yijia
  • Pedersen, Hal

Abstract

This paper proposes a stochastic mortality model featuring both permanent longevity jump and temporary mortality jump processes. A trend reduction component describes unexpected mortality improvement over an extended period of time. The model also captures the uneven effect of mortality events on different ages and the correlations among them. The model will be useful in analyzing future mortality dependent cash flows of life insurance portfolios, annuity portfolios, and portfolios of mortality derivatives. We show how to apply the model to analyze and price a longevity security.

Suggested Citation

  • Cox, Samuel H. & Lin, Yijia & Pedersen, Hal, 2010. "Mortality risk modeling: Applications to insurance securitization," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 242-253, February.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:1:p:242-253
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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, vol. 73(4), pages 647-672, December.
    2. Sithole, Terry Z. & Haberman, Steven & Verrall, Richard J., 2000. "An investigation into parametric models for mortality projections, with applications to immediate annuitants' and life office pensioners' data," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 285-312, December.
    3. Darius Lakdawalla & Tomas Philipson, 2002. "The Rise in Old-Age Longevity and the Market for Long-Term Care," American Economic Review, American Economic Association, vol. 92(1), pages 295-306, March.
    4. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    5. Oecd, 2006. "Overview of the Financial Wealth Accumulated under Funded," Financial Market Trends, OECD Publishing, vol. 2006(2), pages 189-221.
    6. Helmut Gründl & Thomas Post & Roman N. Schulze, 2006. "To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 19-41, March.
    7. Samuel Cox & Yijia Lin, 2007. "Natural Hedging of Life and Annuity Mortality Risks," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 1-15.
    8. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Estimating the term structure of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 492-504, April.
    9. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    10. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    11. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
    12. Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736, December.
    13. Vaupel, James W, 1998. "Demographic Analysis of Aging and Longevity," American Economic Review, American Economic Association, vol. 88(2), pages 242-247, May.
    14. Renshaw, A.E. & Haberman, S. & Hatzopoulos, P., 1996. "The Modelling of Recent Mortality Trends in United Kingdom Male Assured Lives," British Actuarial Journal, Cambridge University Press, vol. 2(2), pages 449-477, June.
    15. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    16. Ronald Lee, 2000. "The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(1), pages 80-91.
    17. Lin, Yijia & Cox, Samuel H., 2008. "Securitization of catastrophe mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 628-637, April.
    18. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    19. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
    20. 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.
    21. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
    22. Stephen Goss & Alice Wade & Felicitie Bell & Bernard Dussault, 1998. "Historical and Projected Mortality for Mexico, Canada, and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(4), pages 108-126.
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