Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion
In this paper, we discuss a generalization of the collective risk model and of Panjer’s recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim causes ha...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/8/2/43 |
| _version_ | 1797569092101603328 |
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| author | Cordelia Rudolph Uwe Schmock |
| author_facet | Cordelia Rudolph Uwe Schmock |
| author_sort | Cordelia Rudolph |
| collection | DOAJ |
| description | In this paper, we discuss a generalization of the collective risk model and of Panjer’s recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim causes have certain dependence structures and prove that Panjer’s recursion is also applicable by finding an appropriate equivalent representation of the claim numbers. These dependence structures are of a stochastic non-negative linear nature and may also produce negative correlations between the claim causes. The consideration of risk groups also includes dependence between claim sizes. Compounding the claim causes by common distributions also keeps Panjer’s recursion applicable. |
| first_indexed | 2024-03-10T20:06:06Z |
| format | Article |
| id | doaj.art-ffb10a1b560a4c0dac9e6eb84031d732 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-10T20:06:06Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-ffb10a1b560a4c0dac9e6eb84031d7322023-11-19T23:19:43ZengMDPI AGRisks2227-90912020-05-01824310.3390/risks8020043Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s RecursionCordelia Rudolph0Uwe Schmock1msg life Austria Ges.m.b.H., Ausstellungsstraße 50, 1020 Vienna, AustriaDepartment of Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8–10/E105-1, 1040 Vienna, AustriaIn this paper, we discuss a generalization of the collective risk model and of Panjer’s recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim causes have certain dependence structures and prove that Panjer’s recursion is also applicable by finding an appropriate equivalent representation of the claim numbers. These dependence structures are of a stochastic non-negative linear nature and may also produce negative correlations between the claim causes. The consideration of risk groups also includes dependence between claim sizes. Compounding the claim causes by common distributions also keeps Panjer’s recursion applicable.https://www.mdpi.com/2227-9091/8/2/43extended CreditRisk+Poisson mixture distributiondependence modellingcompound distributionPanjer recursion |
| spellingShingle | Cordelia Rudolph Uwe Schmock Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion Risks extended CreditRisk+ Poisson mixture distribution dependence modelling compound distribution Panjer recursion |
| title | Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion |
| title_full | Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion |
| title_fullStr | Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion |
| title_full_unstemmed | Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion |
| title_short | Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion |
| title_sort | multivariate collective risk model dependent claim numbers and panjer s recursion |
| topic | extended CreditRisk+ Poisson mixture distribution dependence modelling compound distribution Panjer recursion |
| url | https://www.mdpi.com/2227-9091/8/2/43 |
| work_keys_str_mv | AT cordeliarudolph multivariatecollectiveriskmodeldependentclaimnumbersandpanjersrecursion AT uweschmock multivariatecollectiveriskmodeldependentclaimnumbersandpanjersrecursion |