20.500.12556/RUL-131795 Utežne funkcije v klasičnem procesu tveganja magistrsko delo Scale functions in the classical risk process Verjetnost propada zavarovalnice je pomembna količina, ki jo spremljajo njeni delničarji kot tudi regulatorji. Klasična teorija tveganja opiše proces gibanja višine kapitala s Cramér-Lundbergovim procesom. V tem delu bodo predstavljene utežne funkcije in njihove osnovne lastnosti ter uporaba v eno-stranskih in dvo-stranskih izhodnih problemih. Z utežnimi funkcijami bo tudi razvita Gerber-Shiujeva teorija tveganja za klasični proces tveganja. Z njo bodo analizirani čas propada, primanjkljaj ob propadu in višina kapitala tik pred propadom. Klasična teorija bo nadgrajena s tremi perturbacijami poti, ki se lahko prevedejo na probleme dividendnih in obdavčitvenih politik v zavarovalništvu. Pri teh strategijah bo izračunana verjetnost propada in pričakovana sedanja vrednost izplačil (dividend ali davkov) do propada. Probability of ruin of insurance company plays an important role for its shareholders and regulators. Classical risk theory describes evolution of wealth or surplus with Cramér-Lundberg process. Scale functions and their characteristics will be presented in this work as well as their use in one-sided and two-sided exit problems. Scale functions will also be applied in Gerber-Shiu risk theory for classical risk process. Time of ruin, deficit at ruin and surplus prior to ruin will be analysed with Gerber-Shiu risk theory. Classical theory will be upgraded with three path perturbations, which can translate to dividend and tax policies in insurance. In these strategies probability of ruin and expected present value of payouts (dividends or taxes) until ruin will be computed. utežne funkcije klasični proces tveganja Cramér-Lundbergov proces dividendni problem obdavčitveni problem zavarovalništvo propad Gerber-Shiujeva mera scale functions classical risk process Cramér-Lundberg process dividend problem taxation problem insurance ruin Gerber-Shiu measure true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2021-10-03 08:15:03 2021-10-03 08:15:04 2024-05-29 12:45:40 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.8 121592 79024643 3809.pdf 3809.pdf 1 5963C6D1F93DC88EAACB5D8766FBB646 622eb2b126223c7848d310a0bc83d97b7d77ecfac977633ca8b867164720ecef f5f48471-2410-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=149204 Fakulteta za matematiko in fiziko 0 0 0