Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-04-30T21:01:57.617Z Has data issue: false hasContentIssue false
  • English
  • Français

Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims

Published online by Cambridge University Press:  24 April 2023

Jonas Crevecoeur Open the ORCID record for Jonas Crevecoeur [Opens in a new window] ,
Katrien Antonio ,
Stijn Desmedt  and
Alexandre Masquelein
Jonas Crevecoeur
Affiliation:
Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
Katrien Antonio*
Affiliation:
Faculty of Economics and Business, KU Leuven, Leuven, Belgium Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands LRisk, Leuven Research Center on Insurance and Financial Risk Analysis, KU Leuven, Leuven, Belgium LStat, Leuven Statistics Research Center, KU Leuven, Leuven, Belgium
Stijn Desmedt
Affiliation:
QBE Re, Bruxelles, Belgium
Alexandre Masquelein
Affiliation:
QBE Re, Bruxelles, Belgium
*
*Corresponding author. E-Mail: katrien.antonio@kuleuven.be
Get access Rights & Permissions [Opens in a new window]

Abstract

Due to the presence of reporting and settlement delay, claim data sets collected by non-life insurance companies are typically incomplete, facing right censored claim count and claim severity observations. Current practice in non-life insurance pricing tackles these right censored data via a two-step procedure. First, best estimates are computed for the number of claims that occurred in past exposure periods and the ultimate claim severities, using the incomplete, historical claim data. Second, pricing actuaries build predictive models to estimate technical, pure premiums for new contracts by treating these best estimates as actual observed outcomes, hereby neglecting their inherent uncertainty. We propose an alternative approach that brings valuable insights for both non-life pricing and reserving. As such, we effectively bridge these two key actuarial tasks that have traditionally been discussed in silos. Hereto, we develop a granular occurrence and development model for non-life claims that tackles reserving and at the same time resolves the inconsistency in traditional pricing techniques between actual observations and imputed best estimates. We illustrate our proposed model on an insurance as well as a reinsurance portfolio. The advantages of our proposed strategy are most compelling in the reinsurance illustration where large uncertainties in the best estimates originate from long reporting and settlement delays, low claim frequencies and heavy (even extreme) claim sizes.

Keywords

Non-life pricingnon-life reservingstatistical and machine learning methodsreinsuranceoccurrencereporting and development of claims
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 2 , May 2023 , pp. 185 - 212
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albrecher, H., Beirlant, J. and Teugels, J.L. (2017) Reinsurance: Actuarial and Statistical Aspects. Wiley Series in Probability and Statistics. John Wiley & Sons Ltd. URL https://doi.org/10.1002/9781119412540.Google Scholar
Albrecher, H. and Bladt, M. (2022) Informed censoring: The parametric combination of data and expert information. URL https://arxiv.org/pdf/2206.13091.pdf.Google Scholar
Crevecoeur, J., Robben, J. and Antonio, K. (2022) A hierarchical reserving model for non-life insurance claims. Insurance: Mathematics and Economics. URL https://doi.org/10.1016/j.insmatheco.2022.02.005.Google Scholar
Delong, L., Lindholm, M. and Wüthrich, M.V. (2022) Collective reserving using individual claims data. Scandinavian Actuarial Journal, (1), 1–28. URL https://doi.org/10.1080/03461238.2021.1921836.CrossRefGoogle Scholar
Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22. URL https://doi.org/10.1111/j.2517-6161.1977.tb01600.x.Google Scholar
Denuit, M., Marechal, X., Pitrebois, S. and Walhin, J.-F. (2007) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems, 1 edition. West Sussex: John Wiley & Sons Ltd. ISBN 9780470026779.CrossRefGoogle Scholar
Frees, E.W. and Valdez, E.A. (2008) Hierarchical insurance claims modeling. Journal of the American Statistical Association, 103 (484), 1457–1469. URL https://doi.org/10.1198/016214508000000823.CrossRefGoogle Scholar
Friedman, J.H. (2001) Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5), 1189–1232. URL https://doi.org/10.1214/aos/1013203451.CrossRefGoogle Scholar
Jensen, J. (1906) Sur les fonctions convexes et les inégalités entre les valeurs moyennese. Acta Mathematica, 30, 175–193. URL https://doi.org/10.1007/BF02418571.CrossRefGoogle Scholar
Jewell, W.S. (1990) Predicting IBNYR events and delays. ASTIN Bulletin, 20, 93–111. URL https://doi.org/10.2143/AST.19.1.2014914.CrossRefGoogle Scholar
Kalbfleisch, J.D. and Lawless, J.F. (1991) Regression models for right truncated data with applications to AIDS incubation times and reporting lags. Statistica Sinica, 1(1), 19–32. URL http://www.jstor.org/stable/24303991.Google Scholar
Larsen, C.R. (2007) An individual claims reserving model. ASTIN Bulletin, 37(1), 113–132.CrossRefGoogle Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23, 213–225. URL https://doi.org/10.2143/AST.23.2.2005092.CrossRefGoogle Scholar
Mack, T. (1999) The standard error of chain ladder reserve estimates: Recursive calculation and inclusion of a tail factor. ASTIN Bulletin, 29, 361–366. URL https://doi.org/10.2143/AST.29.2.504622.CrossRefGoogle Scholar
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin, 23(1), 95–115. URL https://doi.org/10.2143/AST.23.1.2005103.CrossRefGoogle Scholar
Norberg, R. (1999) Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bulletin, 29(1), 5–27. URL https://doi.org/10.2143/AST.29.1.504603.CrossRefGoogle Scholar
Verbelen, R., Antonio, K., Claeskens, G. and Crevecoeur, J. (2022) Modeling the occurrence of events subject to a reporting delay via an EM algorithm. Statistical Science, 37(3), 394–410.CrossRefGoogle Scholar
Wüthrich, M.V. (2018) Machine learning in individual claims reserving. Scandinavian Actuarial Journal, 2018(6), 465–480.CrossRefGoogle Scholar