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Comonotonic approximations to quantiles of life annuity conditional expected present value

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  • Denuit, Michel

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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  • Denuit, Michel, 2008. "Comonotonic approximations to quantiles of life annuity conditional expected present value," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 831-838, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:831-838
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    References listed on IDEAS

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    1. Carlos Wong-Fupuy & Steven Haberman, 2004. "Projecting Mortality Trends," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 56-83.
    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.
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    5. 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.
    6. 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.
    7. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    8. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
    9. 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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    Cited by:

    1. Alai, Daniel H. & Landsman, Zinoviy & Sherris, Michael, 2016. "Modelling lifetime dependence for older ages using a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 272-285.
    2. Michel Denuit, 2009. "Life Anuities with Stochastic Survival Probabilities: A Review," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 463-489, September.
    3. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
    4. Liu, Xiaoming & Jang, Jisoo & Mee Kim, Sun, 2011. "An application of comonotonicity theory in a stochastic life annuity framework," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 271-279, March.
    5. Stevens, R.S.P. & De Waegenaere, A.M.B. & Melenberg, B., 2011. "Longevity Risk and Natural Hedge Potential in Portfolios Of Life Insurance Products : The Effect of Investment Risk," Other publications TiSEM a3e07689-4b6b-4987-852c-3, Tilburg University, School of Economics and Management.
    6. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.
    7. Alai, Daniel H. & Landsman, Zinoviy & Sherris, Michael, 2013. "Lifetime dependence modelling using a truncated multivariate gamma distribution," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 542-549.
    8. Stevens, R.S.P. & De Waegenaere, A.M.B. & Melenberg, B., 2011. "Longevity Risk and Natural Hedge Potential in Portfolios Of Life Insurance Products : The Effect of Investment Risk," Discussion Paper 2011-036, Tilburg University, Center for Economic Research.
    9. Gbari, Samuel & Denuit, Michel, 2014. "Efficient approximations for numbers of survivors in the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 71-77.

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