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Distributions suitable for modelling of individual losses
Janáková, Veronika ; Staňková Helisová, Kateřina (referee) ; Mazurová, Lucie (advisor)
Nazov prace: Ro/dclenia vhodne k modelovaniu vysky skod Autor: Veronika Janakova Katedra: Katcdra pravdepodobnosti a matematickcj statistiky VedoLici bakalarskej prace: RNDr. LucJc Mazurova, Ph.D e-mail vcduecho: Mazurova@karlin.nifT.cuni.cz Abstrakt: Obsahom prace jc prchfad rozdeleni vyu/ivanych v oblasti nezivotneho poistenia na modclovanic vysky skod. V iivode si definujcme zakladnc rozdclenia, ktore naslednc transfbrniujcme. Pri kazdom rozdeleni su uvcdcnc zakladne charakteristiky, ktorymi je dane rozdelenie urcenc. Ccla praca jc rozdclcna do dvoch kapitol. V prvcj kapitole sa zameriame na dcfim'cie u/ spominanych zakladnych rozdeleni a v druhcj casti prace budeme zakladne rozdelenia transibrmovaf. Vyuzijeme dva druhy transtbrmacii, pomocou ktorych ziskamc rozdelcnia s viaeerymi parametrami. Takcto rozdelenia maju sirsie pouzitie, leda su llexibilnejsie a mnoho rozdcleni ziskame ako spceialne pripady. KTucove slova: pravdepodobnostne rozdelenia, transformacia Title: Distributions suitable for modelling of individual losses Author: Veronika Janakova Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurova, Ph.D Supervisor's e-mail address: Mazurova@karHn.mff.euni.cz Abstract: Subject of this paper is to provide a review of distribution used in the section of...
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Mortality projection methods
Kuběnová, Věra ; Mazurová, Lucie (referee) ; Netolická, Hana (advisor)
In this thesis we study the issue of mortality projection.We introduce some basic terms related to mortality, describe life tables and special attention is paid to generation life tables. We are interested in an important phenomenon of so-called cohort effect which influences the mortality projection. There are also discussed possible reasons for creation of the cohort effect. We use available data for population of the Czech Republic for looking into existence of the cohort effect in Czech population. For comparison we mention the existence of the cohort effect in other developed countries.We study different approaches mortality model and project.We set up various factors influencing mortality patterns and the way of their analyzing by some scientific branches. Some of the mortality projection methods are described in more detail. The Lee-Carter method is chosen to forecast mortality for population of the Czech Republic in period 2007-2060.
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Risk Process with Random Income
Ringlerová, Anna ; Mazurová, Lucie (referee) ; Klebanov, Lev (advisor)
This diploma thesis deals with risk processes. It describes a classical risk process and mentions the ruin probability. A convolution formula and the Beekman convolution formula for calculating the ruin probability are deduced for the classical risk process. The following part of the thesis provides the investigation of the Cram¶er-Lundberg, the Beekman-Bowers and the De Vylder approximation to the ruin probability. The accuracy of approximations is illustrated in two examples. Afterwards, a risk process with random income is studied and a convolution formula for such a process is derived. In an example, the classical risk process is taken as a specic type of the risk process with random income. For such a process, the ruin probability computed by the convolution formula for classical risk process is compared to the ruin probability computed by the convolution formula for the risk process with random income. It is shown that sometimes the ruin probability is undervalued when computed by the convolution formula for classical risk process.
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