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Modelling dependent data for longevity projections


  • D’Amato, Valeria
  • Haberman, Steven
  • Piscopo, Gabriella
  • Russolillo, Maria


The risk profile of an insurance company involved in annuity business is heavily affected by the uncertainty in future mortality trends. It is problematic to capture accurately future survival patterns, in particular at retirement ages when the effects of the rectangularization phenomenon and random fluctuations are combined. Another important aspect affecting the projections is related to the so-called cohort-period effect. In particular, the mortality experience of countries in the industrialized world over the course of the twentieth century would suggest a substantial age–time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. Also the dependence between ages is an important component in the modeling of mortality (Barrieu et al., 2011). It is observed that the mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, 2008). Moreover, considering the data subdivided by set by single years of age, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. The aim of this paper is to improve the methodology for forecasting mortality in order to enhance model performance and increase forecasting power by capturing the dependence structure of neighboring observations in the population. To do this, we adapt the methodology for measuring uncertainty in projections in the Lee–Carter context and introduce a tailor-made bootstrap instead of an ordinary bootstrap. The approach is illustrated with an empirical example.

Suggested Citation

  • D’Amato, Valeria & Haberman, Steven & Piscopo, Gabriella & Russolillo, Maria, 2012. "Modelling dependent data for longevity projections," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 694-701.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:694-701
    DOI: 10.1016/j.insmatheco.2012.09.008

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    References listed on IDEAS

    1. Renshaw, A. E. & Haberman, S., 2003. "On the forecasting of mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 379-401, July.
    2. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    3. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    4. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.
    5. Arthur Renshaw & Steven Haberman, 2003. "Lee-Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 119-137.
    6. Renshaw, A.E. & Haberman, S., 2008. "On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 797-816, April.
    7. 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.
    8. Edwin Choi & Peter Hall, 2000. "Bootstrap confidence regions computed from autoregressions of arbitrary order," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 461-477.
    9. 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.
    10. 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.
    11. Frank Denton & Christine Feaver & Byron Spencer, 2005. "Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy," Journal of Population Economics, Springer;European Society for Population Economics, vol. 18(2), pages 203-227, June.
    12. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
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    Cited by:

    1. Leng, Xuan & Peng, Liang, 2016. "Inference pitfalls in Lee–Carter model for forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 58-65.
    2. 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.
    3. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    4. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 110-124.
    5. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.

    More about this item


    Longevity; Dependence; Lee–Carter; Bootstrap;


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