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arXiv · 2409.12896

Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays

Hassan Abdelrahman·Andrei Badescu·Radu Craiu·Sheldon Lin
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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.

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Hassan Abdelrahman, Andrei Badescu, Radu Craiu, Sheldon Lin. 2024-09-19. Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays. https://doi.org/10.1017/asb.2025.10056

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