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Individual Loss Reserving with the Multivariate Skew Normal Framework

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  • Pigeon, Mathieu
  • Antonio, Katrien
  • Denuit, Michel

Abstract

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims developing in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses development factors similar to those of the well-known chain–ladder method. We suggest the Multivariate Skew Normal distribution as a multivariate distribution suitable for modeling these development factors. Empirical analysis using a real portfolio and out-of-sample prediction tests demonstrate the relevance of the model proposed.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2013. "Individual Loss Reserving with the Multivariate Skew Normal Framework," LIDAM Reprints ISBA 2013028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2013028
    Note: In : ASTIN Bulletin, vol. 43, no. 3, p. 399-428 (2013)
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    Cited by:

    1. 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.
    2. Peng Shi & Glenn M. Fung & Daniel Dickinson, 2022. "Assessing hail risk for property insurers with a dependent marked point process," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 302-328, January.
    3. Andrea Gabrielli & Mario V. Wüthrich, 2018. "An Individual Claims History Simulation Machine," Risks, MDPI, vol. 6(2), pages 1-32, March.
    4. 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.
    5. Denuit, Michel & Trufin, Julien, 2016. "Collective Loss Reserving with Two Types of Claims in Motor Third Party Liability Insurance," LIDAM Discussion Papers ISBA 2016029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
    7. Matias Leppisaari, 2013. "Modeling catastrophic deaths using EVT with a microsimulation approach to reinsurance pricing," Papers 1310.8604, arXiv.org.
    8. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    9. 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.
    10. Alexandre Brouste & Christophe Dutang, 2016. "Closed-form and numerical computations of actuarial indicators in ruin theory and claim reserving," Post-Print hal-01616192, HAL.
    11. Huang, Jinlong & Wu, Xianyi & Zhou, Xian, 2016. "Asymptotic behaviors of stochastic reserving: Aggregate versus individual models," European Journal of Operational Research, Elsevier, vol. 249(2), pages 657-666.
    12. 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.
    13. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    14. Richard J. Verrall & Mario V. Wüthrich, 2016. "Understanding Reporting Delay in General Insurance," Risks, MDPI, vol. 4(3), pages 1-36, July.
    15. 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.
    16. 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.
    17. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    18. Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
    19. 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.
    20. Greg Taylor, 2019. "Loss Reserving Models: Granular and Machine Learning Forms," Risks, MDPI, vol. 7(3), pages 1-18, July.
    21. 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.
    22. 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.
    23. Marie Michaelides & Mathieu Pigeon & H'el`ene Cossette, 2022. "Individual Claims Reserving using Activation Patterns," Papers 2208.08430, arXiv.org, revised Aug 2023.
    24. 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.
    25. Gao, Lisa & Shi, Peng, 2022. "Leveraging high-resolution weather information to predict hail damage claims: A spatial point process for replicated point patterns," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 161-179.

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