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

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<title>Marked Cox models for IBNR claims count: continuous and discretized approaches with Dirichlet-driven reporting delays</title>
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<namePart>Abdelrahman, Hassan</namePart>
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<abstract displayLabel="Summary">This paper introduces a new micro-level Cox model for estimating incurred-but-not-reported (IBNR) claim counts using a hidden Markov model structure. The model is first developed in continuous time to incorporate temporal dependence and policyholder-specific risk factors, but practical challenges arise due to likelihood maximization and right-truncated reporting delays. To address these issues, the authors propose two discrete-time alternatives: one that uses a Dirichlet distribution to capture random variability in reporting delays, and one without this component. EM-based estimation procedures are provided for all models. When applied to an auto-insurance dataset, the discrete-time models outperform the continuous-time version by jointly modeling claim occurrence and reporting delay, with the Dirichlet-based model offering improved flexibility and capturing additional uncertainty. Overall, the framework enhances accuracy in IBNR reserving and can be adapted to different levels of granularity within an insurance portfolio</abstract>
<note type="statement of responsibility">Hassan Abdelrahman... [et al.]</note>
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<topic>Modelos estadísticos</topic>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
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<text>19/01/2026 Volume 56 Issue 1 - January 2026 , p. 60 - 80</text>
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