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

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<rdf:Description>
<dc:creator>Abdelrahman, Hassan</dc:creator>
<dc:creator>International Actuarial Association</dc:creator>
<dc:date>2026-01-15</dc:date>
<dc:description xml:lang="es">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</dc:description>
<dc:identifier>https://documentacion.fundacionmapfre.org/documentacion/publico/es/bib/189428.do</dc:identifier>
<dc:language>eng</dc:language>
<dc:rights xml:lang="es">InC - http://rightsstatements.org/vocab/InC/1.0/</dc:rights>
<dc:subject xml:lang="es">Seguros no vida</dc:subject>
<dc:subject xml:lang="es">Modelos estadísticos</dc:subject>
<dc:subject xml:lang="es">Cálculo actuarial</dc:subject>
<dc:subject xml:lang="es">Riesgo actuarial</dc:subject>
<dc:subject xml:lang="es">Matemática del seguro</dc:subject>
<dc:subject xml:lang="es">Modelo de Markov</dc:subject>
<dc:type xml:lang="es">Artículos y capítulos</dc:type>
<dc:title xml:lang="es">Marked Cox models for IBNR claims count: continuous and discretized approaches with Dirichlet-driven reporting delays</dc:title>
<dc:relation xml:lang="es">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</dc:relation>
</rdf:Description>
</rdf:RDF>