Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays
Abstract
Accurate loss reserving is crucial in Property and Casualty (P&C) insurance for financial stability, regulatory compliance, and effective risk management. We propose a novel micro-level Cox model based on hidden Markov models (HMMs). 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.
Cite
@article{arxiv.2409.12896,
title = {Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays},
author = {Hassan Abdelrahman and Andrei Badescu and Radu Craiu and Sheldon Lin},
journal= {arXiv preprint arXiv:2409.12896},
year = {2026}
}