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Predicting IBNYR Events and Delays II. Discrete Time

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  • Jewell, William S.

Abstract

An IBNYR event is one that occurs randomly during some fixed exposure interval and incurs a random delay before it is reported. A previous paper developed a continuous-time model of the IBNYR process in which both the Poisson rate at which events occur and the parameters of the delay distribution are unknown random quantities; a full-distributional Bayesian method was then developed to predict the number of unreported events. Using a numerical example, the success of this approach was shown to depend upon whether or not the occurrence dates were available in addition to the reporting dates. This paper considers the more usual practical situation in which only discretized epoch information is available; this leads to a loss of predictive accuracy, which is investigated by considering various levels of quantization for the same numerical example.

Suggested Citation

  • Jewell, William S., 1990. "Predicting IBNYR Events and Delays II. Discrete Time," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 93-111, April.
    • Handle: RePEc:cup:astinb:v:20:y:1990:i:01:p:93-111_00
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    Citations

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    Cited by:

    1. 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.
    2. Peng Shi, 2017. "A Multivariate Analysis of Intercompany Loss Triangles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 717-737, June.
    3. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    4. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    5. 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.
    6. Richard J. Verrall & Mario V. Wüthrich, 2016. "Understanding Reporting Delay in General Insurance," Risks, MDPI, vol. 4(3), pages 1-36, July.
    7. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2018. "Dynamic and granular loss reserving with copulae," Papers 1801.01792, arXiv.org.
    8. 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.
    9. Crevecoeur, Jonas & Antonio, Katrien & Desmedt, Stijn & Masquelein, Alexandre, 2023. "Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims," ASTIN Bulletin, Cambridge University Press, vol. 53(2), pages 185-212, May.
    10. 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.
    11. 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.
    12. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2019. "Infinitely Stochastic Micro Forecasting," Papers 1908.10636, arXiv.org, revised Sep 2019.

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