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

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Denuit, Michel [UCL] Haberman, Steven Renshaw, Arthur E.

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès interdit
Publication date 2013
Language Anglais
Journal information "European Actuarial Journal" - Vol. 3, no. 1, p. 191-201 (2013)
Peer reviewed yes
issn 2190-9733
e-issn 2190-9741
Publication status Publié
Affiliation UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords Life annuity ; Life expectancy ; Mortality projection ; Comonotonicity ; Simulation
Links
  1. Brouhns Natacha, Denuit Michel, Vermunt Jeroen K., A Poisson log-bilinear regression approach to the construction of projected lifetables, 10.1016/s0167-6687(02)00185-3
  2. Denuit Michel, Distribution of the random future life expectancies in log-bilinear mortality projection models, 10.1007/s10985-007-9040-6
  3. Denuit Michel, Dhaene Jan, Comonotonic bounds on the survival probabilities in the Lee–Carter model for mortality projection, 10.1016/j.cam.2006.03.015
  4. Denuit M., Dhaene J., Goovaerts M., Kaas R., Actuarial Theory for Dependent Risks : Measures, Orders and Models, ISBN:9780470016459, 10.1002/0470016450
  5. Denuit M., Haberman S., Renshaw A.E., Comonotonic Approximations to Quantiles of Life Annuity Conditional Expected Present Values: Extensions to General Arima Models and Comparison with the Bootstrap, 10.2143/ast.40.1.2049232
  6. Haberman Steven, Renshaw Arthur, Parametric mortality improvement rate modelling and projecting, 10.1016/j.insmatheco.2011.11.005
  7. Lee RD, Carter L (1992) Modelling and forecasting the time series of US mortality. J Am Stat Assoc 87:659–675 (with discussion)
  8. Renshaw A.E., Haberman S., Lee–Carter mortality forecasting with age-specific enhancement, 10.1016/s0167-6687(03)00138-0
Bibliographic reference Denuit, Michel ; Haberman, Steven ; Renshaw, Arthur E.. Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach to modelling and projecting mortality. In: European Actuarial Journal, Vol. 3, no. 1, p. 191-201 (2013)
Permanent URL http://hdl.handle.net/2078.1/133117