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A parameterized approach to modeling and forecasting mortality

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  • Hatzopoulos, P.
  • Haberman, S.

Abstract

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085-1111] or equivalently as a generalized Lee-Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751-2006) and Greece (1957-2006).

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  • 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.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:1:p:103-123
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    3. Ahmadi, Seyed Saeed & Li, Johnny Siu-Hang, 2014. "Coherent mortality forecasting with generalized linear models: A modified time-transformation approach," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 194-221.
    4. Bozikas, Apostolos & Pitselis, Georgios, 2020. "Incorporating crossed classification credibility into the Lee–Carter model for multi-population mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 353-368.
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    6. Alex Isakson & Simone Krummaker & María Dolores Martínez-Miranda & Ben Rickayzen, 2021. "Calendar Effect and In-Sample Forecasting Applied to Mesothelioma Mortality Data," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
    7. Hong Li & Johnny Siu-Hang Li, 2017. "Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements," Demography, Springer;Population Association of America (PAA), vol. 54(3), pages 1073-1095, June.
    8. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    9. Ufuk Beyaztas & Hanlin Shang, 2022. "Machine-Learning-Based Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Forecasting, MDPI, vol. 4(1), pages 1-15, March.
    10. Apostolos Bozikas & Georgios Pitselis, 2018. "An Empirical Study on Stochastic Mortality Modelling under the Age-Period-Cohort Framework: The Case of Greece with Applications to Insurance Pricing," Risks, MDPI, vol. 6(2), pages 1-34, April.
    11. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    12. George Mavridoglou & Peter Kiochos, 2011. "Sickness recovery intensities for short term health insurance in Greece," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 61(1-2), pages 39-54, january -.
    13. Valeria D’Amato & Steven Haberman & Gabriella Piscopo & Maria Russolillo, 2014. "Computational framework for longevity risk management," Computational Management Science, Springer, vol. 11(1), pages 111-137, January.
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    15. Hatzopoulos, P. & Haberman, S., 2013. "Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 320-337.

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