Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T09:50:21.066Z Has data issue: false hasContentIssue false

Mortality Projection Based on the Wang Transform

Published online by Cambridge University Press:  17 April 2015

Piet De Jong
Affiliation:
Department of Actuarial Studies, Macquarie University, NSW 2109, Australia, Email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A new method for analysing and projecting mortality is proposed and examined. The method takes observed time series of survival probabilities, finds the corresponding z-scores in the standard normal distribution and forecasts the z-scores. The z-scores appear to follow a common simple linear progression in time and hence forecasting is straightforward. Analysis on the z-score scale offers useful insights into the way mortality evolves over time. The method and extensions are applied to Australian female mortality data to derive projections to the year 2100 in both survival probabilities and expectations of life.

Type
Articles
Copyright
Copyright © ASTIN Bulletin 2007

References

Arnold, L. (1974) Stochastic Differential Equations: Theory and Applications. New York: John Wiley.Google Scholar
Bowers, J.N., Gerber, H., Hickman, J., Jones, D. and Nesbitt, C. (1997) Actuarial Mathematics. Schaumburg, IL: Society of Actuaries.Google Scholar
De Boor, C. (1978) A Practical Guide to Splines. New York: Springer.CrossRefGoogle Scholar
De Jong, P. (1989) Smoothing and interpolation with the state-space model. Journal of the American Statistical Association 84(408), 10851088.CrossRefGoogle Scholar
De Jong, P. and Mazzi, S. (2001) Modelling and smoothing unequally spaced sequence data. Statistical Inference for Stochastic Processes 4(1), 5371.CrossRefGoogle Scholar
De Jong, P. and Penzer, J.R. (1998) Diagnosing shocks in time series. Journal of the American Statistical Association 93(442), 796806.CrossRefGoogle Scholar
De Jong, P. and Tickle, L. (2006) Extending the Lee Carter model of mortality projection. Mathematical Population Studies 13(1), 118.CrossRefGoogle Scholar
Harvey, A.C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.Google Scholar
Heligman, L. and Pollard, J.H. (1980) The age pattern of mortality. Journal of the Institute of Actuaries 107, 4980.CrossRefGoogle Scholar
Lee, R.D. and Carter, L.W. (1992) Modelling and forecasting U.S. mortality (with discussion). Journal of the American Statistical Association 87(419), 659675.Google Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models (2d ed.). New York: Chapman and Hall.CrossRefGoogle Scholar
McNown, R. and Rogers, A. (1989) Forecasting mortality: A parameterized time series approach. Demography 26(4), 645660.CrossRefGoogle ScholarPubMed
Wang, S.S. (2000) A class of distortion operators for pricing financial and insurance risks. The Journal of Risk and Insurance 67(2), 1536.CrossRefGoogle Scholar