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Marked Cox models for IBNR claims count: continuous and discretized approaches with Dirichlet-driven reporting delays
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MAP20260002002
Marked Cox models for IBNR claims count: continuous and discretized approaches with Dirichlet-driven reporting delays / Hassan Abdelrahman... [et al.]
Sumario: 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
En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 19/01/2026 Volume 56 Issue 1 - January 2026 , p. 60 - 80
1. Seguros no vida ‌. 2. Modelos estadísticos ‌. 3. Cálculo actuarial ‌. 4. Riesgo actuarial ‌. 5. Matemática del seguro ‌. 6. Modelo de Markov ‌. I. Abdelrahman, Hassan ‌. II. International Actuarial Association ‌.