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A TREE-BASED ALGORITHM ADAPTED TO MICROLEVEL RESERVING AND LONG DEVELOPMENT CLAIMS

Published online by Cambridge University Press:  07 May 2019

Olivier Lopez ,
Xavier Milhaud Open the ORCID record for Xavier Milhaud [Opens in a new window]  and
Pierre-E. Thérond
Olivier Lopez
Affiliation:
Sorbonne Université, CNRS Laboratoire de Probabilités Statistique et Modélisation LPSM, 4 place Jussieu F-75005 Paris, France
Xavier Milhaud*
Affiliation:
Université de Lyon Université Claude Bernard Lyon1 ISFA, LSAF, F-69007, Lyon, France E-Mail: xavier.milhaud@univ-lyon1.fr
Pierre-E. Thérond
Affiliation:
Galea & Associés 25 rue de Choiseul 75002, Paris, France
*
E-mail: xavier.milhaud@univ-lyon1.fr
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Abstract

In non-life insurance, business sustainability requires accurate and robust predictions of reserves related to unpaid claims. To this aim, two different approaches have historically been developed: aggregated loss triangles and individual claim reserving. The former has reached operational great success in the past decades, whereas the use of the latter still remains limited. Through two illustrative examples and introducing an appropriate tree-based algorithm, we show that individual claim reserving can be really promising, especially in the context of long-term risks.

Keywords

Reservinglong tailcensoringregression treedisability
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 741 - 762
Copyright
© Astin Bulletin 2019 

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Footnotes

*

The affiliation for Pierre-E. Thérond has been updated since this article’s original publication. An erratum detailing this change has also been published. See https://doi.org/10.1017/asb.2019.21.

References

Antonio, K. and Plat, R. (2014) Micro-level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal, 2014 (7), 649–669.CrossRefGoogle Scholar
Baudry, M. and Robert, C.Y. (2017) Non parametric individual claim reserving in insurance. Working paper.Google Scholar
Bornhuetter, R. and Ferguson, R.E. (1972) The actuary and IBNR. Casualty Actuarial Society, 59, 181–195.Google Scholar
Breiman, L., Friedman, J., Olshen, R.A. and Stone, C.J. (1984) Classification and Regression Trees. Boca Raton, FL: Chapman and Hall.Google Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance (with discussion). British Actuarial Journal, 8 (3), 443–544.CrossRefGoogle Scholar
Haastrup, S. and Arjas, E. (1993) Claims reserving in continuous time: A nonparametric Bayesian approach. ASTIN Bulletin, 2, 139–164.Google Scholar
Halliwell, L.J. (2007) Chain-ladder bias: Its reason and meaning. Variance, 1 (2), 214–247. doi: 10.1080/03461238.2018.1428681.Google Scholar
Harnau, J. (2017) Misspecification tests for chain-ladder models. Technical Report 840, Discussion Paper Series, Department of Economics, University of Oxford.Google Scholar
Larsen, C. (2007) An individual claims reserving model. ASTIN Bulletin, 37 (1), 113–132.CrossRefGoogle Scholar
Lopez, O. (2018) A censored copula model for micro-level claim reserving. Working paper or preprint, February. URL: https://hal.archives-ouvertes.fr/hal-01706935.Google Scholar
Lopez, O., Milhaud, X. and Therond, P-E. (2016) Tree-based censored regression with applications in insurance. Electronic Journal of Statistics, 10, 2685–2716. dx.doi.org/10.1214/16-EJS1189.CrossRefGoogle Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain-ladder reserve estimates. ASTIN Bulletin, 23, 213–225.CrossRefGoogle Scholar
Olbricht, W. (2012) Tree-based methods: A useful tool for life insurance. European Actuarial Journal, 2 (1), 129–147. doi: 10.1007/s13385-012-0045-5.CrossRefGoogle Scholar
Pigeon, M., Antonio, K. and Denuit, M. (2013) Individual loss reserving with the multivariate skew normal framework. ASTIN Bulletin, 43 (3), 399–428.CrossRefGoogle Scholar
Quarg, G. and Mack, T. (2008) Munich chain ladder: A reserving method that reduces the gap between IBNR projections based on paid losses and IBNR projections based on incurred losses. Variance, 2 (2), 266–299.Google Scholar
Wüthrich, M.V. (2018a) Machine learning in individual claims reserving. Scandinavian Actuarial Journal, 2018 (6), 465–480. doi: 10.1080/03461238.2018.1428681.CrossRefGoogle Scholar
Wüthrich, M.V. (2018b) Neural networks applied to chain-ladder reserving. European Actuarial Journal, 8 (2), 407–436. doi: 10.1007/s13385-018-0184-4.CrossRefGoogle Scholar
Zhao, X.B., Zhou, X. and Wang, J.L. (2009) Semiparametric model for prediction of individual claim loss reserving. Insurance: Mathematics and Economics, 45 (1), 1–8.Google Scholar