An Observation-Driven State-Space Model for Claims Size Modeling
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929651831537664 |
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| author | Ahn, Jae Youn Jeong, Himchan Wüthrich, Mario V. |
| author_facet | Ahn, Jae Youn Jeong, Himchan Wüthrich, Mario V. |
| contents | State-space models are popular models in econometrics. Recently, these models have gained some popularity in the actuarial literature. The best known state-space models are of Kalman-filter type. These models are so-called parameter-driven because the observations do not impact the state-space dynamics. A second less well-known class of state-space models are so-called observation-driven state-space models where the state-space dynamics is also impacted by the actual observations. A typical example is the Poisson-Gamma observation-driven state-space model for counts data. This Poisson-Gamma model is fully analytically tractable. The goal of this paper is to develop a Gamma- Gamma observation-driven state-space model for claim size modeling. We provide fully tractable versions of Gamma-Gamma observation-driven state-space models, and these versions extend the work of Smith and Miller (1986) by allowing for a fully flexible variance behavior. Additionally, we demonstrate that the proposed model aligns with evolutionary credibility, a methodology in insurance that dynamically adjusts premium rates over time using evolving data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Observation-Driven State-Space Model for Claims Size Modeling Ahn, Jae Youn Jeong, Himchan Wüthrich, Mario V. Methodology Applications State-space models are popular models in econometrics. Recently, these models have gained some popularity in the actuarial literature. The best known state-space models are of Kalman-filter type. These models are so-called parameter-driven because the observations do not impact the state-space dynamics. A second less well-known class of state-space models are so-called observation-driven state-space models where the state-space dynamics is also impacted by the actual observations. A typical example is the Poisson-Gamma observation-driven state-space model for counts data. This Poisson-Gamma model is fully analytically tractable. The goal of this paper is to develop a Gamma- Gamma observation-driven state-space model for claim size modeling. We provide fully tractable versions of Gamma-Gamma observation-driven state-space models, and these versions extend the work of Smith and Miller (1986) by allowing for a fully flexible variance behavior. Additionally, we demonstrate that the proposed model aligns with evolutionary credibility, a methodology in insurance that dynamically adjusts premium rates over time using evolving data. |
| title | An Observation-Driven State-Space Model for Claims Size Modeling |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2412.21099 |