Analysis of an aggregate loss model in a Markov renewal regime
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911770715619328 |
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| author | Ramírez-Cobo, Pepa Carrizosa, Emilio Lillo, Rosa Elvira |
| author_facet | Ramírez-Cobo, Pepa Carrizosa, Emilio Lillo, Rosa Elvira |
| contents | In this article we consider an aggregate loss model with dependent losses. The losses occurrence process is governed by a two-state Markovian arrival process (MAP2), a Markov renewal process process that allows for (1) correlated inter-losses times, (2) non-exponentially distributed inter-losses times and, (3) overdisperse losses counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real operational risk database, the aggregate loss model is estimated by fitting separately the inter-losses times and severities. The MAP2 is estimated via direct maximization of the likelihood function, and severities are modeled by the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the fit provided by the Poisson process, the results point out that taking into account the dependence and overdispersion in the inter-losses times distribution leads to higher capital charges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14553 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of an aggregate loss model in a Markov renewal regime Ramírez-Cobo, Pepa Carrizosa, Emilio Lillo, Rosa Elvira Risk Management Applications In this article we consider an aggregate loss model with dependent losses. The losses occurrence process is governed by a two-state Markovian arrival process (MAP2), a Markov renewal process process that allows for (1) correlated inter-losses times, (2) non-exponentially distributed inter-losses times and, (3) overdisperse losses counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real operational risk database, the aggregate loss model is estimated by fitting separately the inter-losses times and severities. The MAP2 is estimated via direct maximization of the likelihood function, and severities are modeled by the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the fit provided by the Poisson process, the results point out that taking into account the dependence and overdispersion in the inter-losses times distribution leads to higher capital charges. |
| title | Analysis of an aggregate loss model in a Markov renewal regime |
| topic | Risk Management Applications |
| url | https://arxiv.org/abs/2401.14553 |