Prague Economic Papers 2017, 26(5):542-560 | DOI: 10.18267/j.pep.625

Stochastic Claims Reserving in Insurance Using Random Effects

Michal Gerthofer1, Michal Pešta2
1 Faculty of Informatics and Statistics, Department of Statistics and Probability, University of Economics in Prague, Prague, Czech Republic (Michal.Gerthofer@gmail.com)
2 Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University in Prague, Prague, Czech Republic (Michal.Pesta@mff.cuni.cz)

Estimation of claims reserves, which should be held by the insurer so as to be able to meet expected future claims arising from policies currently in force and policies written in the past, presents an important task for insurance companies to predict their liabilities. A common approach to the reser-ving problem is based on generalized linear models (GLM). In this article, the application of genera-lized linear mixed models (GLMM) - an extension of the GLM - for estimation of the loss reserves is shown. Since the GLMM allows incorporating a random effect instead of several fixed effects corresponding to the accident years as in case of the GLM, volatility of the prediction is reduced. This allows more flexible risk valuation, which is a crucial element of risk management and capital allocation practices of non-life insurers. A real data example together with diagnostics for the model selection are provided as an illustration of the potential benefits of the presented approach.

Keywords: claims reserving, non-life insurance, dependency modelling, random effects, mixed models, GLM, GLMM, panel data
JEL classification: C13, C18, C23, C33, C51, G22

Published: October 1, 2017  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
Gerthofer, M., & Pešta, M. (2017). Stochastic Claims Reserving in Insurance Using Random Effects. Prague Economic Papers, 26(5), 542-560. doi: 10.18267/j.pep.625
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. Antonio, K., Beirlant, J. (2007). Actuarial Statistics with Generalized Linear Mixed Models. Insurance: Mathematics and Economics, 40(1), 58-76, https://doi.org/10.1016/j.insmatheco.2006.02.013 Go to original source...
    2. Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, H. H., White, J. S. (2009). Generalized Linear Mixed Models: A Practical Guide for Ecology and Evolution. Trends in Ecology and Evolution, 24(3), 127-135, https://doi.org/10.1016/j.tree.2008.10.008 Go to original source...
    3. Diggle, P. J., Heagerty, P., Liang, K. Y., Zeger, S. (2002). Analysis of Longitudinal Data. 2nd Edition. New York: Oxford University Press. Go to original source...
    4. Dobson, A. J. (2002). An Introduction to Generalized Linear Models. Boca Raton: CRC Press. England, P. D., Verrall, R. J. (2002). Stochastic Claims Reserving in General Insurance. British Actuarial Journal, 8(3), 443-518, https://doi.org/10.1017/s1357321700003809 Go to original source...
    5. Fitzmaurice, G. M., Laird, N. M., Ware, J. H. (2004). Applied Longitudinal Analysis. Boston: John Wiley and Sons.
    6. Greene, W. H. (2002). Econometric Analysis. New Jersey: Prentice Hall. Go to original source...
    7. Hudecová, Š., Pešta, M. (2013). Modelling Dependencies in Claims Reserving with GEE. Insurance: Mathematics and Economics, 53(3), 786-794, https://doi.org/10.1016/j.insmatheco.2013.09.018 Go to original source...
    8. Lehmann, E. L. (1983). Theory of Point Estimation. New York: Wiley. Go to original source...
    9. McCulloch, C. E., Searle, S. (2001). Generalized Linear and Mixed Models. Boston: John Wiley and Sons. Go to original source...
    10. Meyers, G. G., Shi, P. (2011). Loss Reserving Data Pulled from NAIC Schedule P. [Online; Updated September 01, 2011; Accessed June 10, 2014]. Available at: http://www.casact.org/research/index.cfm?fa=loss_reserves_data
    11. Pešta, M., Okhrin, O. (2014). Conditional Least Squares and Copulae in Claims Reserving for a Single Line of Business. Insurance: Mathematics and Economics, 56(1), 28-37, https://doi.org/10.1016/j.insmatheco.2014.02.007 Go to original source...
    12. Rabe-Hesketh, S., Skrondal, A. (2002). Reliable Estimation of Generalized Linear Mixed Models Using Adaptive Quadrature. The Stata Journal, 2(1), 1-21. Available at: http://ageconsearch.umn.edu/bitstream/115947/2/sjart_st0005.pdf Go to original source...
    13. Rao, C. R., Toutenburg, H., Fieger, A., Heumann, C., Nittner, T., Scheid, S. (1999). Linear Models: Least Squares and Alternatives. 2nd Edition. Hoboken: Wiley Finance.
    14. Raudenbush, S. (2000). Maximum Likelihood for Generalized Linear Models with Nested Random Effects via High-Order, Multivariate Laplace Approximation. Journal of Computational and Graphical Statistics, 9(1), 141-157, https://doi.org/10.2307/1390617 Go to original source...
    15. Wüthrich, M. V, Merz, M. (2008). Stochastic Claims Reserving Methods in Insurance. Hoboken: Wiley Finance.

    This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY NC ND 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content