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Prediction of RBNS and IBNR Claims using Claim Amounts and Claim Counts

Author

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  • Verrall, Richard
  • Nielsen, Jens Perch
  • Jessen, Anders Hedegaard

Abstract

A model is proposed using the run-off triangle of paid claims and also the numbers of reported claims (in a similar triangular array). These data are usually available, and allow the model proposed to be implemented in a large variety of situations. On the basis of these data, the stochastic model is built from detailed assumptions for individual claims, but then approximated using a compound Poisson framework. The model explicitly takes into account the delay from when a claim is incurred and to when it is reported (the IBNR delay) and the delay from when a claim is reported and to when it is fully paid (the RBNS delay). These two separate sources of delay are estimated separately, unlike most other reserving methods. The results are compared with those of the chain ladder technique.

Suggested Citation

  • Verrall, Richard & Nielsen, Jens Perch & Jessen, Anders Hedegaard, 2010. "Prediction of RBNS and IBNR Claims using Claim Amounts and Claim Counts," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 871-887, November.
    • Handle: RePEc:cup:astinb:v:40:y:2010:i:02:p:871-887_00
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Jonas Harnau, 2018. "Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models," Risks, MDPI, vol. 6(2), pages 1-25, March.
    4. 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.
    5. Wahl, Felix, 2019. "Explicit moments for a class of micro-models in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 140-156.
    6. Jonas Harnau, 2018. "Log-Normal or Over-Dispersed Poisson?," Risks, MDPI, vol. 6(3), pages 1-37, July.
    7. Wahl, Felix & Lindholm, Mathias & Verrall, Richard, 2019. "The collective reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 34-50.
    8. 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.
    9. Lindholm, Mathias & Verrall, Richard, 2020. "Regression based reserving models and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 109-124.
    10. Huang, Jinlong & Qiu, Chunjuan & Wu, Xianyi & Zhou, Xian, 2015. "An individual loss reserving model with independent reporting and settlement," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 232-245.
    11. 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.

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