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Marked Cox models for IBNR claims count: continuous and discretized approaches with Dirichlet-driven reporting delays

Hassan Abdelrahman et al.

ASTIN Bulletin2025https://doi.org/10.1017/asb.2025.10056article
AJG 2ABDC A*
Weight
0.41

Abstract

We propose a novel micro-level Cox model for incurred but not reported (IBNR) claims count based on hidden Markov models. Initially formulated as a continuous-time model, it addresses the complexity of incorporating temporal dependencies and policyholder risk attributes. However, the continuous-time model faces significant challenges in maximizing the likelihood and fitting right-truncated reporting delays. To overcome these issues, we introduce two discrete-time versions: one incorporating unsystematic randomness in reporting delays through a Dirichlet distribution and one without. We provide the EM algorithm for parameter estimation for all three models and apply them to an auto-insurance dataset to estimate IBNR claim counts. Our results show that while all models perform well, the discrete-time versions demonstrate superior performance by jointly modeling delay and frequency, with the Dirichlet-based model capturing additional variability in reporting delays. This approach enhances the accuracy and reliability of IBNR reserving, offering a flexible framework adaptable to different levels of granularity within an insurance portfolio.

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https://doi.org/https://doi.org/10.1017/asb.2025.10056

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@article{hassan2025,
  title        = {{Marked Cox models for IBNR claims count: continuous and discretized approaches with Dirichlet-driven reporting delays}},
  author       = {Hassan Abdelrahman et al.},
  journal      = {ASTIN Bulletin},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1017/asb.2025.10056},
}

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Evidence weight

0.41

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.25 × 0.4 = 0.10
M · momentum0.55 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.