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Utežne funkcije v klasičnem procesu tveganja : magistrsko delo
ID Horvat, Leon (Author), ID Vidmar, Matija (Mentor) More about this mentor... This link opens in a new window

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Abstract
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.

Language:Slovenian
Keywords:utežne funkcije, klasični proces tveganja, Cramér-Lundbergov proces, dividendni problem, obdavčitveni problem, zavarovalništvo, propad, Gerber-Shiujeva mera
Work type:Master's thesis/paper
Organization:FMF - Faculty of Mathematics and Physics
Year:2021
PID:20.500.12556/RUL-131795 This link opens in a new window
UDC:519.8
COBISS.SI-ID:79024643 This link opens in a new window
Publication date in RUL:03.10.2021
Views:667
Downloads:71
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Secondary language

Language:English
Title:Scale functions in the classical risk process
Abstract:
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.

Keywords:scale functions, classical risk process, Cramér-Lundberg process, dividend problem, taxation problem, insurance, ruin, Gerber-Shiu measure

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