##### Proces rizika s náhodným příjmem
 dc.contributor.advisor Klebanov, Lev dc.creator Ringlerová, Anna dc.date.accessioned 2017-04-06T11:41:04Z dc.date.available 2017-04-06T11:41:04Z dc.date.issued 2007 dc.identifier.uri http://hdl.handle.net/20.500.11956/13298 dc.description.abstract 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. en_US dc.language English cs_CZ dc.language.iso en_US dc.publisher Univerzita Karlova, Matematicko-fyzikální fakulta cs_CZ dc.title Risk Process with Random Income en_US dc.type diplomová práce cs_CZ dcterms.created 2007 dcterms.dateAccepted 2007-09-24 dc.description.department Katedra pravděpodobnosti a matematické statistiky cs_CZ dc.description.department Department of Probability and Mathematical Statistics en_US dc.description.faculty Faculty of Mathematics and Physics en_US dc.description.faculty Matematicko-fyzikální fakulta cs_CZ dc.identifier.repId 42806 dc.title.translated Proces rizika s náhodným příjmem cs_CZ dc.contributor.referee Mazurová, Lucie dc.identifier.aleph 000939641 thesis.degree.name Mgr. thesis.degree.level magisterské cs_CZ thesis.degree.discipline Finanční a pojistná matematika cs_CZ thesis.degree.discipline Financial and insurance mathematics en_US thesis.degree.program Mathematics en_US thesis.degree.program Matematika cs_CZ uk.thesis.type diplomová práce cs_CZ uk.taxonomy.organization-cs Matematicko-fyzikální fakulta::Katedra pravděpodobnosti a matematické statistiky cs_CZ uk.taxonomy.organization-en Faculty of Mathematics and Physics::Department of Probability and Mathematical Statistics en_US uk.faculty-name.cs Matematicko-fyzikální fakulta cs_CZ uk.faculty-name.en Faculty of Mathematics and Physics en_US uk.faculty-abbr.cs MFF cs_CZ uk.degree-discipline.cs Finanční a pojistná matematika cs_CZ uk.degree-discipline.en Financial and insurance mathematics en_US uk.degree-program.cs Matematika cs_CZ uk.degree-program.en Mathematics en_US thesis.grade.cs Dobře cs_CZ thesis.grade.en Good en_US uk.abstract.en 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. en_US uk.publication.place Praha cs_CZ uk.grantor Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra pravděpodobnosti a matematické statistiky cs_CZ dc.identifier.lisID 990009396410106986
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