Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911372956139520 |
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| author | Abdelrahman, Hassan Badescu, Andrei Craiu, Radu Lin, Sheldon |
| author_facet | Abdelrahman, Hassan Badescu, Andrei Craiu, Radu Lin, Sheldon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12896 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays Abdelrahman, Hassan Badescu, Andrei Craiu, Radu Lin, Sheldon Applications 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. |
| title | Marked Cox Models for IBNR Claims Count: Continuous and Discretized Approaches with Dirichlet-Driven Reporting Delays |
| topic | Applications |
| url | https://arxiv.org/abs/2409.12896 |