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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.14985 |
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| _version_ | 1866909354545905664 |
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| author | Fleck, Andrew Furman, Edward Shen, Yang |
| author_facet | Fleck, Andrew Furman, Edward Shen, Yang |
| contents | Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc).
We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14985 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Loss Reserving: Dependence and Estimation Fleck, Andrew Furman, Edward Shen, Yang Methodology Risk Management Applications 91B30 Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc). We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical. |
| title | Stochastic Loss Reserving: Dependence and Estimation |
| topic | Methodology Risk Management Applications 91B30 |
| url | https://arxiv.org/abs/2410.14985 |