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Comonotonic approximations to quantiles of life annuity conditional expected present value

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  • Denuit, Michel
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    Abstract

    In large portfolios, the risk borne by annuity providers (insurance companies or pension funds) is basically driven by the randomness in the future mortality rates. To fix the ideas, we adopt here the standard Lee-Carter framework, where the future forces of mortality are decomposed in a log-bilinear way. This paper aims to provide accurate approximations for the quantiles of the conditional expected present value of the payments to the annuity provider, given the future path of the Lee-Carter time index. Mortality is stochastic while the discount factors are derived from a zero-coupon yield curve and are assumed to be deterministic. Numerical illustrations based on Belgian mortality (general population and insurance market statistics) show that the accuracy of the approximations proposed in this paper is remarkable, with relative difference less than 1% for most probability levels.

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    Bibliographic Info

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

    Volume (Year): 42 (2008)
    Issue (Month): 2 (April)
    Pages: 831-838

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:831-838

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

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    1. Kaas, R & Dhaene, Jan & Goovaerts, Marc, 2000. "Upper and lower bounds for sums of random variables," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/223713, Katholieke Universiteit Leuven.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    3. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    5. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    6. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
    7. 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.
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