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Velké odchylky a jejich aplikace v pojistné matematice / Large deviations and their applications in insurance mathematics

Title: Large deviations and their applications in insurance mathematics Author: Lucia Fuchsová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Zbyněk Pawlas, Ph.D. Supervisor's e-mail address: Zbynek.Pawlas@mff.cuni.cz Abstract: In the present work we study large deviations theory. We discuss heavy-tailed distributions, which describe the probability of large claim oc- curence. We are interested in the use of large deviations theory in insurance. We simulate claim sizes and their arrival times for Cramér-Lundberg model and first we analyze the probability that ruin happens in dependence on the parameters of our model for Pareto distributed claim size, next we compare ruin probability for other claim size distributions. For real life data we model the probability of large claim size occurence by generalized Pareto distribu- tion. 1

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:295955
Date January 2011
CreatorsFuchsová, Lucia
ContributorsPawlas, Zbyněk, Klebanov, Lev
Source SetsCzech ETDs
LanguageSlovak
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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