Advertisement

European Actuarial Journal

, Volume 8, Issue 2, pp 407–436 | Cite as

Neural networks applied to chain–ladder reserving

  • Mario V. WüthrichEmail author
Original Research Paper
  • 138 Downloads

Abstract

Classical claims reserving methods act on so-called claims reserving triangles which are aggregated insurance portfolios. A crucial assumption in classical claims reserving is that these aggregated portfolios are sufficiently homogeneous so that a coarse reserving algorithm can be applied. We start from such a coarse reserving method, which in our case is Mack’s chain–ladder method, and show how this approach can be refined for heterogeneity and individual claims feature information using neural networks.

Keywords

Claims reserving Mack’s CL model Individual claims reserving Micro-level reserving Neural networks Individual claims features Claims covariates 

Notes

Acknowledgements

We would like to kindly thank Philipp Reinmann (AXA) and Ronald Richman (AIG) who have provided very useful remarks on previous versions of this manuscript.

References

  1. 1.
    Antonio K, Plat R (2014) Micro-level stochastic loss reserving for general insurance. Scand Act J 2014(7):649–669MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arjas E (1989) The claims reserving problem in non-life insurance: some structural ideas. ASTIN Bull 19(2):139–152MathSciNetCrossRefGoogle Scholar
  3. 3.
    Badescu AL, Lin XS, Tang D (2016) A marked Cox model for the number of IBNR claims: theory. Insur Math Econ 69:29–37MathSciNetCrossRefGoogle Scholar
  4. 4.
    Badescu AL, Lin XS, Tang D (2016) A marked Cox model for the number of IBNR claims: estimation and application. Version March 14, 2016. SSRN Manuscript 2747223Google Scholar
  5. 5.
    Baudry M, Robert CY (2017) Non parametric individual claim reserving in insurance. PreprintGoogle Scholar
  6. 6.
    Cybenko G (1989) Approximation by superpositions of a sigmoidal function. MCSS 2/4:303–314MathSciNetzbMATHGoogle Scholar
  7. 7.
    Gabrielli A, Wüthrich MV (2018) An individual claims history simulation machine. Risks 6(2):29CrossRefGoogle Scholar
  8. 8.
    Harej B, Gächter R, Jamal S (2017) Individual claim development with machine learning. ASTIN ReportGoogle Scholar
  9. 9.
    Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366CrossRefGoogle Scholar
  10. 10.
    Isenbeck M, Rüschendorf L (1992) Completeness in location families. Prob Math Stat 13:321–343MathSciNetzbMATHGoogle Scholar
  11. 11.
    Jessen AH, Mikosch T, Samorodnitsky G (2011) Prediction of outstanding payments in a Poisson cluster model. Scand Act J 2011(3):214–237MathSciNetCrossRefGoogle Scholar
  12. 12.
    LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444CrossRefGoogle Scholar
  13. 13.
    Lopez O (2018) A censored copula model for micro-level claim reserving. HAL Id: hal-01706935Google Scholar
  14. 14.
    Mack T (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bull 23(2):213–225MathSciNetCrossRefGoogle Scholar
  15. 15.
    Montúfar G, Pascanu R, Cho K, Bengio Y (2014) On the number of linear regions of deep neural networks. Neural Inf Process Syst Proc \({}^{\beta }\) 27:2924–2932Google Scholar
  16. 16.
    Nielsen M (2017) Neural networks and deep learning. Online book available on http://neuralnetworksanddeeplearning.com
  17. 17.
    Norberg R (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bull 23(1):95–115CrossRefGoogle Scholar
  18. 18.
    Norberg R (1999) Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bulletin 29(1):5–25CrossRefGoogle Scholar
  19. 19.
    Pigeon M, Antonio K, Denuit M (2013) Individual loss reserving with the multivariate skew normal framework. ASTIN Bull 43(3):399–428MathSciNetCrossRefGoogle Scholar
  20. 20.
    Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(6088):533–536CrossRefGoogle Scholar
  21. 21.
    Schnieper R (1991) Separating true IBNR and IBNER claims. ASTIN Bull 21(1):111–127MathSciNetCrossRefGoogle Scholar
  22. 22.
    Verrall RJ, Wüthrich MV (2016) Understanding reporting delay in general insurance. Risks 4(3):25CrossRefGoogle Scholar
  23. 23.
    Werbos P (1982) Applications of advances in nonlinear sensitivity analysis. Syst Model Optim 1982:762–770CrossRefGoogle Scholar
  24. 24.
    Wüthrich MV (2018) Machine learning in individual claims reserving. Scand Act J 2018(6):465–480MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zarkadoulas A (2017) Neural network algorithms for the development of individual losses. MSc thesis, University of LausanneGoogle Scholar

Copyright information

© EAJ Association 2018

Authors and Affiliations

  1. 1.Department of MathematicsETH Zurich, RiskLabZurichSwitzerland

Personalised recommendations