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A linear algebraic method for pricing temporary life annuities and insurance policies

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  • Date, P.
  • Mamon, R.
  • Jalen, L.
  • Wang, I.C.
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    Abstract

    We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims.

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    Bibliographic Info

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

    Volume (Year): 47 (2010)
    Issue (Month): 1 (August)
    Pages: 98-104

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    Handle: RePEc:eee:insuma:v:47:y:2010:i:1:p:98-104

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

    Related research

    Keywords: Stochastic interest rate models Stochastic mortality models Annuity pricing Insurance premium;

    References

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    1. Olivieri, Annamaria & Pitacco, Ermanno, 2008. "Assessing the cost of capital for longevity risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(3), pages 1013-1021, June.
    2. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 77-105, January.
    3. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 38(1), pages 81-97, February.
    4. 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.
    5. Burnecki, Krzysztof & Marciniuk, Agnieszka & Weron, Aleksander, 2003. "Annuities under random rates of interest--revisited," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 32(3), pages 457-460, July.
    6. Zaks, Abraham, 2001. "Annuities under random rates of interest," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 28(1), pages 1-11, February.
    7. 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.
    8. 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, Elsevier, vol. 31(3), pages 373-393, December.
    9. 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.
    10. 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.
    11. Gaillardetz, Patrice, 2008. "Valuation of life insurance products under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(1), pages 212-226, February.
    12. Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 385-423.
    13. Date, P. & Mamon, R. & Wang, I.C., 2007. "Valuation of cash flows under random rates of interest: A linear algebraic approach," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 41(1), pages 84-95, July.
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