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Computational framework for longevity risk management

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  • Valeria D’Amato

    ()

  • Steven Haberman

    ()

  • Gabriella Piscopo

    ()

  • Maria Russolillo

    ()

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    Abstract

    Longevity risk threatens the financial stability of private and government sponsored defined benefit pension systems as well as social security schemes, in an environment already characterized by persistent low interest rates and heightened financial uncertainty. The mortality experience of countries in the industrialized world 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. It is observed that mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, Integrating financial and demographic longevity risk models: an Australian model for financial applications, Discussion Paper PI-0817, 2008 ). Moreover, considering the dataset by single ages, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., J Population Econ 18:203–227, 2005 ). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the “lack of dependence” (Denuit et al., Actuarial theory for dependent risks: measures. Orders and models, Wiley, New York, 2005 ). By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun, J Probability Stat, 813583:15, 2010 ), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving confidence intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence. Copyright Springer-Verlag Berlin Heidelberg 2014

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    Bibliographic Info

    Article provided by Springer in its journal Computational Management Science.

    Volume (Year): 11 (2014)
    Issue (Month): 1 (January)
    Pages: 111-137

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    Handle: RePEc:spr:comgts:v:11:y:2014:i:1:p:111-137

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    Related research

    Keywords: Longevity risk management; Bootstrap techniques;

    References

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    1. PALM, Franz, . "On univariate time series methods and simultaneous equation econometric models," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -293, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Econometric Society World Congress 2000 Contributed Papers 1585, Econometric Society.
    3. 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.
    4. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 96-45, Board of Governors of the Federal Reserve System (U.S.).
    5. 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.
    6. Hatzopoulos, P. & Haberman, S., 2009. "A parameterized approach to modeling and forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 103-123, February.
    7. 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, Springer, vol. 18(2), pages 203-227, 06.
    8. 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.
    9. 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.
    10. 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.
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