[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2108.07924.html
   My bibliography  Save this paper

Stochastic loss reserving with mixture density neural networks

Author

Listed:
  • Muhammed Taher Al-Mudafer
  • Benjamin Avanzi
  • Greg Taylor
  • Bernard Wong
Abstract
Neural networks offer a versatile, flexible and accurate approach to loss reserving. However, such applications have focused primarily on the (important) problem of fitting accurate central estimates of the outstanding claims. In practice, properties regarding the variability of outstanding claims are equally important (e.g., quantiles for regulatory purposes). In this paper we fill this gap by applying a Mixture Density Network ("MDN") to loss reserving. The approach combines a neural network architecture with a mixture Gaussian distribution to achieve simultaneously an accurate central estimate along with flexible distributional choice. Model fitting is done using a rolling-origin approach. Our approach consistently outperforms the classical over-dispersed model both for central estimates and quantiles of interest, when applied to a wide range of simulated environments of various complexity and specifications. We further extend the MDN approach by proposing two extensions. Firstly, we present a hybrid GLM-MDN approach called "ResMDN". This hybrid approach balances the tractability and ease of understanding of a traditional GLM model on one hand, with the additional accuracy and distributional flexibility provided by the MDN on the other. We show that it can successfully improve the errors of the baseline ccODP, although there is generally a loss of performance when compared to the MDN in the examples we considered. Secondly, we allow for explicit projection constraints, so that actuarial judgement can be directly incorporated in the modelling process. Throughout, we focus on aggregate loss triangles, and show that our methodologies are tractable, and that they out-perform traditional approaches even with relatively limited amounts of data. We use both simulated data -- to validate properties, and real data -- to illustrate and ascertain practicality of the approaches.

Suggested Citation

  • Muhammed Taher Al-Mudafer & Benjamin Avanzi & Greg Taylor & Bernard Wong, 2021. "Stochastic loss reserving with mixture density neural networks," Papers 2108.07924, arXiv.org.
    • Handle: RePEc:arx:papers:2108.07924
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2108.07924
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jacky H. L. Poon, 2019. "Penalising Unexplainability in Neural Networks for Predicting Payments per Claim Incurred," Risks, MDPI, vol. 7(3), pages 1-11, September.
    2. Andrea Gabrielli & Mario V. Wüthrich, 2018. "An Individual Claims History Simulation Machine," Risks, MDPI, vol. 6(2), pages 1-32, March.
    3. Kevin Kuo, 2018. "DeepTriangle: A Deep Learning Approach to Loss Reserving," Papers 1804.09253, arXiv.org, revised Sep 2019.
    4. Denuit, Michel & Hainaut, Donatien & Trufin, Julien, 2020. "Effective Statistical Learning Methods for Actuaries II : Tree-Based Methods and Extensions," LIDAM Reprints ISBA 2020035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Hien D. Nguyen & Geoffrey McLachlan, 2019. "On approximations via convolution-defined mixture models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(16), pages 3945-3955, August.
    6. Tashman, Leonard J., 2000. "Out-of-sample tests of forecasting accuracy: an analysis and review," International Journal of Forecasting, Elsevier, vol. 16(4), pages 437-450.
    7. Ronald Richman & Mario V. Wuthrich, 2021. "LocalGLMnet: interpretable deep learning for tabular data," Papers 2107.11059, arXiv.org.
    8. Kevin Kuo, 2019. "DeepTriangle: A Deep Learning Approach to Loss Reserving," Risks, MDPI, vol. 7(3), pages 1-12, September.
    9. Avanzi, Benjamin & Taylor, Greg & Wang, Melantha & Wong, Bernard, 2021. "SynthETIC: An individual insurance claim simulator with feature control," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 296-308.
    10. Benjamin Avanzi & Gregory Clive Taylor & Melantha Wang & Bernard Wong, 2020. "SynthETIC: an individual insurance claim simulator with feature control," Papers 2008.05693, arXiv.org, revised Aug 2021.
    11. Gabrielli, Andrea, 2020. "A Neural Network Boosted Double Overdispersed Poisson Claims Reserving Model," ASTIN Bulletin, Cambridge University Press, vol. 50(1), pages 25-60, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Benjamin Avanzi & Gregory Clive Taylor & Melantha Wang, 2021. "SPLICE: A Synthetic Paid Loss and Incurred Cost Experience Simulator," Papers 2109.04058, arXiv.org, revised Mar 2022.

    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. Benjamin Avanzi & Yanfeng Li & Bernard Wong & Alan Xian, 2022. "Ensemble distributional forecasting for insurance loss reserving," Papers 2206.08541, arXiv.org, revised Jun 2024.
    2. Avanzi, Benjamin & Taylor, Greg & Wang, Melantha & Wong, Bernard, 2021. "SynthETIC: An individual insurance claim simulator with feature control," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 296-308.
    3. 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.
    4. Greg Taylor, 2019. "Risks Special Issue on “Granular Models and Machine Learning Models”," Risks, MDPI, vol. 8(1), pages 1-2, December.
    5. Valandis Elpidorou & Carolin Margraf & María Dolores Martínez-Miranda & Bent Nielsen, 2019. "A Likelihood Approach to Bornhuetter–Ferguson Analysis," Risks, MDPI, vol. 7(4), pages 1-20, December.
    6. Kevin Kuo & Daniel Lupton, 2020. "Towards Explainability of Machine Learning Models in Insurance Pricing," Papers 2003.10674, arXiv.org.
    7. Xu, Shuzhe & Zhang, Chuanlong & Hong, Don, 2022. "BERT-based NLP techniques for classification and severity modeling in basic warranty data study," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 57-67.
    8. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    9. Gao, Guangyuan & Meng, Shengwang & Shi, Yanlin, 2021. "Dispersion modelling of outstanding claims with double Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 572-586.
    10. Yang Qiao & Chou-Wen Wang & Wenjun Zhu, 2024. "Machine learning in long-term mortality forecasting," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 340-362, April.
    11. Benjamin Avanzi & Gregory Clive Taylor & Melantha Wang, 2021. "SPLICE: A Synthetic Paid Loss and Incurred Cost Experience Simulator," Papers 2109.04058, arXiv.org, revised Mar 2022.
    12. Simon CK Lee, 2020. "Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing," Risks, MDPI, vol. 8(1), pages 1-21, February.
    13. Kelly Burns & Imad Moosa, 2017. "Demystifying the Meese–Rogoff puzzle: structural breaks or measures of forecasting accuracy?," Applied Economics, Taylor & Francis Journals, vol. 49(48), pages 4897-4910, October.
    14. Zan Yu & Lianzeng Zhang, 2024. "Computing the Gerber-Shiu function with interest and a constant dividend barrier by physics-informed neural networks," Papers 2401.04378, arXiv.org.
    15. Mariana Oliveira & Luís Torgo & Vítor Santos Costa, 2021. "Evaluation Procedures for Forecasting with Spatiotemporal Data," Mathematics, MDPI, vol. 9(6), pages 1-27, March.
    16. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    17. Pawlikowski, Maciej & Chorowska, Agata, 2020. "Weighted ensemble of statistical models," International Journal of Forecasting, Elsevier, vol. 36(1), pages 93-97.
    18. Spiliotis, Evangelos & Makridakis, Spyros & Kaltsounis, Anastasios & Assimakopoulos, Vassilios, 2021. "Product sales probabilistic forecasting: An empirical evaluation using the M5 competition data," International Journal of Production Economics, Elsevier, vol. 240(C).
    19. Liang, Chao & Xia, Zhenglan & Lai, Xiaodong & Wang, Lu, 2022. "Natural gas volatility prediction: Fresh evidence from extreme weather and extended GARCH-MIDAS-ES model," Energy Economics, Elsevier, vol. 116(C).
    20. Barrow, Devon K., 2016. "Forecasting intraday call arrivals using the seasonal moving average method," Journal of Business Research, Elsevier, vol. 69(12), pages 6088-6096.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2108.07924. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.