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Life Anuities with Stochastic Survival Probabilities: A Review

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  • Michel Denuit

    (Université Catholique de Louvain)

Abstract

An insurance company selling life annuities has to use projected life tables to describe the survival of policyholders. Such life tables are generated by stochastic processes governing the future path of mortality. To fix the ideas, the standard Lee-Carter model for mortality projection is adopted here. In that context, the paper purposes to examine the consequences of working with random survival probabilities. Various stochastic inequalities are derived, showing that the risk borne by the annuity provider is increased compared to the classical independent case. Moreover, the type of dependence existing between the insured life times is carefully examined. The paper also deals with the computation of ruin probabilities and large portfolio approximations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:3:d:10.1007_s11009-008-9076-4
    DOI: 10.1007/s11009-008-9076-4
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    References listed on IDEAS

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    1. Moshe Shaked & Fabio Spizzichino, 1998. "Positive Dependence Properties of Conditionally Independent Random Lifetimes," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 944-959, November.
    2. H. Panjer, Harry & Shaun Wang,, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 227-258, November.
    3. Carlos Wong-Fupuy & Steven Haberman, 2004. "Projecting Mortality Trends," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 56-83.
    4. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    5. Michel Denuit & Pierre Devolder & Anne‐Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113, March.
    6. 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.
    7. 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.
    8. 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.
    9. Kaas, R & Goovaerts, M, 1985. "Bounds On Distribution Functions Under Integral Constraints," University of Amsterdam, Actuarial Science and Econometrics Archive 293091, University of Amsterdam, Faculty of Economics and Business.
    10. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    11. 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, vol. 73(4), pages 687-718, December.
    12. Frostig, Esther & Denuit, Michel, 2006. "Monotonicity results for portfolios with heterogeneous claims arrival processes," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 484-494, June.
    13. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    14. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
    15. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    16. De Pril, Nelson, 1985. "Recursions for Convolutions of Arithmetic Distributions," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 135-139, November.
    17. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    18. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    19. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
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