| dc.contributor.advisor | Pešta, Michal | |
| dc.creator | Romaňák, Martin | |
| dc.date.accessioned | 2023-07-24T11:57:24Z | |
| dc.date.available | 2023-07-24T11:57:24Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11956/182503 | |
| dc.description.abstract | The thesis examines a model for representing the number of claims after merging or splitting different lines of business of an insurance company. The model is based on count- ing processes, the Poisson and the renewal processes are considered in particular. The operations of superposition and thinning are the proposed solution to this problem. We present the well-known results that the Poisson processes are closed under superposition and several types of thinning and explore the necessary conditions for this statement to also hold for renewal processes. Specifically, the previous work on the superposition of renewal processes is studied and further clarified, and an original result is derived for two types of thinning of a renewal process. The theoretical results are then used to analyze real insurance data in a model situation when an insurance company wants to estimate the future number of claims after merging two of its lines of business. 1 | en_US |
| dc.language | English | cs_CZ |
| dc.language.iso | en_US | |
| dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| dc.subject | counting processes|superposition|thinning|non-life insurance|Poisson process|renewal process | en_US |
| dc.subject | čítací procesy|superpozice|ředění|neživotní pojištění|Poissonův proces|proces obnovy | cs_CZ |
| dc.title | Superposition and thinning of counting processes in non-life insurance | en_US |
| dc.type | bakalářská práce | cs_CZ |
| dcterms.created | 2023 | |
| dcterms.dateAccepted | 2023-06-21 | |
| dc.description.department | Katedra pravděpodobnosti a matematické statistiky | cs_CZ |
| dc.description.department | Department of Probability and Mathematical Statistics | en_US |
| dc.description.faculty | Faculty of Mathematics and Physics | en_US |
| dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
| dc.identifier.repId | 250923 | |
| dc.title.translated | Superpozice a ředění čítacích procesů v neživotním pojištění | cs_CZ |
| dc.contributor.referee | Kříž, Pavel | |
| thesis.degree.name | Bc. | |
| thesis.degree.level | bakalářské | cs_CZ |
| thesis.degree.discipline | Finanční matematika | cs_CZ |
| thesis.degree.discipline | Financial Mathematics | en_US |
| thesis.degree.program | Finanční matematika | cs_CZ |
| thesis.degree.program | Financial Mathematics | en_US |
| uk.thesis.type | bakalářská práce | cs_CZ |
| uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra pravděpodobnosti a matematické statistiky | cs_CZ |
| uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Probability and Mathematical Statistics | en_US |
| uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
| uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
| uk.faculty-abbr.cs | MFF | cs_CZ |
| uk.degree-discipline.cs | Finanční matematika | cs_CZ |
| uk.degree-discipline.en | Financial Mathematics | en_US |
| uk.degree-program.cs | Finanční matematika | cs_CZ |
| uk.degree-program.en | Financial Mathematics | en_US |
| thesis.grade.cs | Výborně | cs_CZ |
| thesis.grade.en | Excellent | en_US |
| uk.abstract.en | The thesis examines a model for representing the number of claims after merging or splitting different lines of business of an insurance company. The model is based on count- ing processes, the Poisson and the renewal processes are considered in particular. The operations of superposition and thinning are the proposed solution to this problem. We present the well-known results that the Poisson processes are closed under superposition and several types of thinning and explore the necessary conditions for this statement to also hold for renewal processes. Specifically, the previous work on the superposition of renewal processes is studied and further clarified, and an original result is derived for two types of thinning of a renewal process. The theoretical results are then used to analyze real insurance data in a model situation when an insurance company wants to estimate the future number of claims after merging two of its lines of business. 1 | en_US |
| uk.file-availability | V | |
| uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra pravděpodobnosti a matematické statistiky | cs_CZ |
| thesis.grade.code | 1 | |
| uk.publication-place | Praha | cs_CZ |
| uk.thesis.defenceStatus | O | |
