Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach for modelling and projecting mortality

Article English OPEN
Haberman, S. ; Denuit, M. ; Renshaw, A. E. (2013)

In this paper, we develop accurate approximations for medians of life expectancy and life annuity pure premiums viewed as functions of future mortality trends as predicted by parametric models of the improvement rates in mortality. Numerical illustrations show that the comonotonic approximations perform well in this case, which suggests that they can be used in practice to evaluate the consequences of the uncertainty in future death rates. Prediction intervals based on 5% and 95% quantiles are also considered but appear to be wider compared to simulated ones. This provides the practitioner with a conservative shortcut, thereby avoiding the problem of simulations within simulations in, for instance, Solvency 2 calculations.
  • References (8)

    Brouhns, N., Denuit, M., Vermunt, J.K. 2002. A Poisson log-bilinear approach to the construction of projected life tables. Insurance: Mathematics and Economics 31, 373-393.

    Denuit, M. 2007. Distribution of the random future life expectancies in log-bilinear mortality projection models. Lifetime Data Analysis, 13, 381-397.

    Denuit, M., Dhaene, J. 2007. Comonotonic bounds on the survival probabilities in the Lee-Carter model for mortality projection. Computational and Applied Mathematics 203, 169-176.

    Denuit, M., Dhaene, J., Goovaerts, M.J., Kaas, R. 2005. Actuarial Theory for Dependent Risks: Measures, Orders and Models. Wiley, New York.

    Denuit, M., Haberman, S., Renshaw A.E. 2010. Comonotonic approximations to quantiles of life annuity conditional expected present values: extensions to general ARIMA models and comparison with the bootstrap. ASTIN Bulletin 40, 331-349.

    Haberman, S., Renshaw A.E. 2009. On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics 45, 255-270.

    Haberman, S., Renshaw A.E. 2012. Parametric mortality improvement rate modelling and projecting. Insurance: Mathematics and Economics 50, 309-333.

    Lee, R.D., Carter, L., 1992. Modelling and forecasting the time series of US mortality. Journal of the American Statistical Association (with discussion) 87, 659-272.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    28
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    City Research Online - IRUS-UK 0 28
Share - Bookmark