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Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts

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  • Daniel J. Geiger

    (Missouri University of Science and Technology)

  • Akim Adekpedjou

    (Missouri University of Science and Technology)

Abstract

We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event’s level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and reported claims.

Suggested Citation

  • Daniel J. Geiger & Akim Adekpedjou, 2022. "Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 815-829, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-022-09950-5
    DOI: 10.1007/s11009-022-09950-5
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    References listed on IDEAS

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    1. 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.
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    6. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    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. Greg Taylor, 2019. "Loss Reserving Models: Granular and Machine Learning Forms," Risks, MDPI, vol. 7(3), pages 1-18, July.
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    Cited by:

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