Superposition and thinning of counting processes in non-life insurance
Superpozice a ředění čítacích procesů v neživotním pojištění
bakalářská práce (OBHÁJENO)
Zobrazit/ otevřít
Trvalý odkaz
http://hdl.handle.net/20.500.11956/182503Identifikátory
SIS: 250923
Kolekce
- Kvalifikační práce [11199]
Autor
Vedoucí práce
Oponent práce
Kříž, Pavel
Fakulta / součást
Matematicko-fyzikální fakulta
Obor
Finanční matematika
Katedra / ústav / klinika
Katedra pravděpodobnosti a matematické statistiky
Datum obhajoby
21. 6. 2023
Nakladatel
Univerzita Karlova, Matematicko-fyzikální fakultaJazyk
Angličtina
Známka
Výborně
Klíčová slova (česky)
čítací procesy|superpozice|ředění|neživotní pojištění|Poissonův proces|proces obnovyKlíčová slova (anglicky)
counting processes|superposition|thinning|non-life insurance|Poisson process|renewal processThe 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