IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i4d10.1007_s00362-025-01715-9.html
   My bibliography  Save this article

Bagging and regression trees in individual claims reserving

Author

Listed:
  • Jan Janoušek

    (Charles University)

  • Michal Pešta

    (Charles University)

Abstract

This methodological paper presents a novel approach to individual claims reserving in non-life insurance, utilizing machine learning techniques. Claims reserving in insurance amounts to stochastically predict the overall loss reserves to cover possible future claims. The developed concepts leverage regression trees and bootstrap aggregating (bagging) to improve the accuracy of reserve predictions. Unlike current approaches focusing solely on the number of claims so far, our approach models both the frequency and severity of claims. Out-of-bag error is employed as a diagnostic tool to enhance model validation. The effectiveness of the proposed methodology is demonstrated through an exemplary data analysis, showcasing its potential to provide more accurate reserve estimates in claims reserving.

Suggested Citation

  • Jan Janoušek & Michal Pešta, 2025. "Bagging and regression trees in individual claims reserving," Statistical Papers, Springer, vol. 66(4), pages 1-26, June.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:4:d:10.1007_s00362-025-01715-9
    DOI: 10.1007/s00362-025-01715-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01715-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-025-01715-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Larsen, Christian Roholte, 2007. "An Individual Claims Reserving Model," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 113-132, May.
    2. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2014. "Individual loss reserving using paid–incurred data," LIDAM Reprints ISBA 2014024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Haastrup, Svend & Arjas, Elja, 1996. "Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 139-164, November.
    4. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    5. Maximilien Baudry & Christian Y. Robert, 2019. "A machine learning approach for individual claims reserving in insurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(5), pages 1127-1155, September.
    6. Massimo De Felice & Franco Moriconi, 2019. "Claim Watching and Individual Claims Reserving Using Classification and Regression Trees," Risks, MDPI, vol. 7(4), pages 1-36, October.
    7. Badescu, Andrei L. & Lin, X. Sheldon & Tang, Dameng, 2016. "A marked Cox model for the number of IBNR claims: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 29-37.
    8. Weisberg, Herbert I & Tomberlin, Thomas J & Chatterjee, Sangit, 1984. "Predicting Insurance Losses under Cross-Classification: A Comparison of Alternative Approaches," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(2), pages 170-178, April.
    9. Taylor, Greg & McGuire, Gráinne & Sullivan, James, 2008. "Individual Claim Loss Reserving Conditioned by Case Estimates," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 215-256, September.
    10. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    11. Hesselager, Ole, 1994. "A Markov Model for Loss Reserving," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 183-193, November.
    12. Richard J. Verrall & Mario V. Wüthrich, 2016. "Understanding Reporting Delay in General Insurance," Risks, MDPI, vol. 4(3), pages 1-36, July.
    13. Anders Jessen & Thomas Mikosch & Gennady Samorodnitsky, 2011. "Prediction of outstanding payments in a Poisson cluster model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2011(3), pages 214-237.
    14. Mario V. Wuthrich & Michael Merz, 2015. "Stochastic Claims Reserving Manual: Advances in Dynamic Modeling," Swiss Finance Institute Research Paper Series 15-34, Swiss Finance Institute.
    15. Katrien Antonio & Richard Plat, 2014. "Micro-level stochastic loss reserving for general insurance," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2014(7), pages 649-669.
    16. Badescu, Andrei L. & Chen, Tianle & Lin, X. Sheldon & Tang, Dameng, 2019. "A Marked Cox Model For The Number Of Ibnr Claims: Estimation And Application," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 709-739, September.
    17. Jewell, William S., 1990. "Predicting IBNYR Events and Delays II. Discrete Time," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 93-111, April.
    18. Michal Gerthofer & Michal Pešta, 2017. "Stochastic Claims Reserving in Insurance Using Random Effects," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(5), pages 542-560.
    19. Zhao, Xiao Bing & Zhou, Xian & Wang, Jing Long, 2009. "Semiparametric model for prediction of individual claim loss reserving," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 1-8, August.
    20. Maciak, Matúš & Mizera, Ivan & Pešta, Michal, 2022. "Functional Profile Techniques For Claims Reserving," ASTIN Bulletin, Cambridge University Press, vol. 52(2), pages 449-482, May.
    21. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    22. Al-Mudafer, Muhammed Taher & Avanzi, Benjamin & Taylor, Greg & Wong, Bernard, 2022. "Stochastic loss reserving with mixture density neural networks," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 144-174.
    23. Zhao, XiaoBing & Zhou, Xian, 2010. "Applying copula models to individual claim loss reserving methods," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 290-299, April.
    24. Jewell, William S., 1989. "Predicting Ibnyr Events and Delays: I. Continuous Time," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 25-55, April.
    25. Lopez, Olivier & Milhaud, Xavier & Thérond, Pierre-E., 2019. "A Tree-Based Algorithm Adapted To Microlevel Reserving And Long Development Claims – Erratum," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 919-919, September.
    26. 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.
    27. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.
    28. Els Godecharle & Katrien Antonio, 2015. "Reserving by Conditioning on Markers of Individual Claims: A Case Study Using Historical Simulation," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(4), pages 273-288, October.
    29. Norberg, Ragnar, 1993. "Prediction of Outstanding Liabilities in Non-Life Insurance1," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 95-115, May.
    30. Lopez, Olivier & Milhaud, Xavier & Thérond, Pierre-E., 2019. "A Tree-Based Algorithm Adapted To Microlevel Reserving And Long Development Claims," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 741-762, September.
    31. Norberg, Ragnar, 1999. "Prediction of Outstanding Liabilities II. Model Variations and Extensions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 5-25, May.
    32. Arjas, Elja, 1989. "The Claims Reserving Problem in Non-Life Insurance: Some Structural Ideas," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 139-152, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    2. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2019. "Infinitely Stochastic Micro Forecasting," Papers 1908.10636, arXiv.org, revised Sep 2019.
    3. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2018. "Dynamic and granular loss reserving with copulae," Papers 1801.01792, arXiv.org.
    4. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    5. Benjamin Avanzi & Gregory Clive Taylor & Bernard Wong & Xinda Yang, 2020. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Papers 2004.11169, arXiv.org, revised Dec 2020.
    6. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    7. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Yang, Xinda, 2021. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 9-24.
    8. Richard J. Verrall & Mario V. Wüthrich, 2016. "Understanding Reporting Delay in General Insurance," Risks, MDPI, vol. 4(3), pages 1-36, July.
    9. Avanzi, Benjamin & Wong, Bernard & Yang, Xinda, 2016. "A micro-level claim count model with overdispersion and reporting delays," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 1-14.
    10. Łukasz Delong & Mario V. Wüthrich, 2020. "Neural Networks for the Joint Development of Individual Payments and Claim Incurred," Risks, MDPI, vol. 8(2), pages 1-34, April.
    11. Crevecoeur, Jonas & Antonio, Katrien & Verbelen, Roel, 2019. "Modeling the number of hidden events subject to observation delay," European Journal of Operational Research, Elsevier, vol. 277(3), pages 930-944.
    12. Yanez, Juan Sebastian & Pigeon, Mathieu, 2021. "Micro-level parametric duration-frequency-severity modeling for outstanding claim payments," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 106-119.
    13. Crevecoeur, Jonas & Robben, Jens & Antonio, Katrien, 2022. "A hierarchical reserving model for reported non-life insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 158-184.
    14. Arthur Charpentier & Mathieu Pigeon, 2016. "Macro vs. Micro Methods in Non-Life Claims Reserving (an Econometric Perspective)," Risks, MDPI, vol. 4(2), pages 1-18, May.
    15. Ihsan Chaoubi & Camille Besse & H'el`ene Cossette & Marie-Pier C^ot'e, 2022. "Micro-level Reserving for General Insurance Claims using a Long Short-Term Memory Network," Papers 2201.13267, arXiv.org.
    16. Fersini, Paola & Melisi, Giuseppe, 2016. "Stochastic model to evaluate the fair value of motor third-party liability under the direct reimbursement scheme and quantification of the capital requirement in a Solvency II perspective," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 27-44.
    17. Badescu, Andrei L. & Lin, X. Sheldon & Tang, Dameng, 2016. "A marked Cox model for the number of IBNR claims: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 29-37.
    18. Marie Michaelides & Mathieu Pigeon & H'el`ene Cossette, 2022. "Individual Claims Reserving using Activation Patterns," Papers 2208.08430, arXiv.org, revised Aug 2023.
    19. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2020. "Stochastic reserving with a stacked model based on a hybridized Artificial Neural Network," Papers 2008.07564, arXiv.org.
    20. Zhao, XiaoBing & Zhou, Xian, 2010. "Applying copula models to individual claim loss reserving methods," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 290-299, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:66:y:2025:i:4:d:10.1007_s00362-025-01715-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.