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In-sample forecasting applied to reserving and mesothelioma mortality

Author

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  • Mammen, Enno
  • Martínez Miranda, María Dolores
  • Nielsen, Jens Perch

Abstract

This paper shows that recent published mortality projections with unobserved exposure can be understood as structured density estimation. The structured density is only observed on a sub-sample corresponding to historical calendar times. The mortality forecast is obtained by extrapolating the structured density to future calendar times using that the components of the density are identified within sample. The new method is illustrated on the important practical problem of forecasting mesothelioma for the UK population. Full asymptotic theory is provided. The theory is given in such generality that it also introduces mathematical statistical theory for the recent continuous chain ladder model. This allows a modern approach to classical reserving techniques used every day in any non-life insurance company around the globe. Applications to mortality data and non-life insurance data are provided along with relevant small sample simulation studies.

Suggested Citation

  • Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:76-86
    DOI: 10.1016/j.insmatheco.2014.12.001
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    References listed on IDEAS

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    1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    2. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
    3. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2013. "Individual Loss Reserving With The Multivariate Skew Normal Framework," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 399-428, September.
    4. Di Kuang & Bent Nielsen & Jens Perch Nielsen, 2011. "Forecasting in an Extended Chain‐Ladder‐Type Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 345-359, June.
    5. Verrall, Richard & Nielsen, Jens Perch & Jessen, Anders Hedegaard, 2010. "Prediction of RBNS and IBNR Claims using Claim Amounts and Claim Counts," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 871-887, November.
    6. repec:wyi:journl:002174 is not listed on IDEAS
    7. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Identification of the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 979-986.
    8. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
    9. D. Kuang & B. Nielsen & J. P. Nielsen, 2009. "Chain-Ladder as Maximum Likelihood Revisited," Economics Papers 2009-W08, Economics Group, Nuffield College, University of Oxford.
    10. Enno Mammen, 2003. "Generalised structured models," Biometrika, Biometrika Trust, vol. 90(3), pages 551-566, September.
    11. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2014. "Individual loss reserving using paid–incurred data," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 121-131.
    12. Miranda, María Dolores Martínez & Nielsen, Bent & Nielsen, Jens Perch & Verrall, Richard, 2011. "Cash Flow Simulation for a Model of Outstanding Liabilities Based on Claim Amounts and Claim Numbers," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 107-129, May.
    13. María Dolores Martínez Miranda & Bent Nielsen & Jens Perch Nielsen, 2015. "Inference and forecasting in the age–period–cohort model with unknown exposure with an application to mesothelioma mortality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(1), pages 29-55, January.
    14. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
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    Citations

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    Cited by:

    1. 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.
    2. Mammen, Enno & Martínez-Miranda, María Dolores & Nielsen, Jens Perch & Vogt, Michael, 2021. "Calendar effect and in-sample forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 31-52.
    3. Zoë Fannon & B. Nielsen, 2018. "Age-period cohort models," Economics Papers 2018-W04, Economics Group, Nuffield College, University of Oxford.
    4. M. Hiabu & E. Mammen & M. D. Martìnez-Miranda & J. P. Nielsen, 2016. "In-sample forecasting with local linear survival densities," Biometrika, Biometrika Trust, vol. 103(4), pages 843-859.
    5. Bischofberger, Stephan M. & Hiabu, Munir & Mammen, Enno & Nielsen, Jens Perch, 2019. "A comparison of in-sample forecasting methods," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 133-154.
    6. Carlo Giovanni Camarda, 2019. "Smooth constrained mortality forecasting," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(38), pages 1091-1130.

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