20.500.12556/DKUM-71000 Sestavljen Poissonov model The compound Poisson model Kadar v vsakdanjem ˇzivljenju govorimo o povsem logiˇcnih sklepih, dostikrat uporabljamo teorijo homogenega Poissonovega procesa, ki ni niˇc drugega kot ime za teorijo ˇstetja pojavov, z doloˇcenimi lastnostmi, ki so najveˇckrat povsem oˇcitne in samoumevne za vsakega posameznika. Po drugi strani pa je za dokazovanje teh oˇcitnih lastnosti, sklepov, potrebne zelo veliko matematike, natanˇcneje teorije verjetnosti. Podobno velja za sestavljen Poissonov model, le da si ga je teˇzje predstavljati in poslediˇcno teˇzje sklepati. Sestavljen Poissonov model govori o gibanju neke vrednosti, katero linearno zvezno poveˇcujemo in hkrati diskretno zmanjˇsujemo v nekih nakljuˇcnih ˇcasih za nakljuˇcne vrednosti. V prvem delu se predstavi homogen Poissonov proces. Zaˇcne se z izrekom, ki pove, kdaj ˇstejemo dogodke, ki so porazdeljeni Poissonovo. Prvi del se nadaljuje z definiranjem lastnosti in konˇca z nazornim primerom. V drugem delu magistrskega dela se najprej navedejo predpostavke sestavljenega Poissonovega modela, ˇcemur sledi definicija. Za predstavitev uporabe sestavljenega Poissonovega modela, sta definirani tudi zelo pomembni porazdelitveni funkciji sluˇcajnih spremenljivk ”verjetnosti in ˇcasa propada”. Delo se nadaljuje z zelo pomembno formulo, s katero se raˇcuna verjetnost propada in konˇca s primeri, katerih verjetnost propada je moˇc izraˇcunati analitiˇcno. When we talk about logics we often think of theory named Homogenious Poisson process. Homogenious Poisson process is nothing more then a name of counting theory with some properties, which are at most obvious and granted for most human beings. On the other hand prooving theese obvious properties is one needs plenty of mathematical knowleadge especially probability theory. The same stands for compound Poisson model just it is harder to imagine it and conclude from it. Compound Poisson model is about a value that is continiously linearly rising and at the same time discretly falling at random times and for random values. In the first part homogenious Poisson process is defined. It starts with the theorem that indicates wheater events are Poisson distributed. It goes on defining properties and ends with ilustrating example. In the second part first the assumptions of compound Poisson model are made which are followed by a definition of a compound Poisson model. For the need of illustrating the useage of compound Poisson model two very important distributions, probability of ruin and time to ruin, are defined. Second part goes on with a very important Pollaczeck-Khinchine formula wich is used for calculating probability of ruin and ends with examples where probability of ruin can be calculated analitically. Poissonov proces sestavljen Poissonov proces zavarovalniˇstvo verjetnost propada ˇcas propada Pollaczeck-Khinchinova formula Poisson process compound Poisson process ensurance probability of ruin time to ruin Pollaczeck-Khinchine formula true true false [J. Šuligoj] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2018-06-28 08:25:23 2018-09-24 11:09:52 2022-08-01 20:15:01 2019-07-11 18:26:57 2018 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 368:519.22(043.2) 24023304 URN:SI:UM:DK:PUQWLZ5B MAG_Suligoj_Jernej_2018.pdf MAG_Suligoj_Jernej_2018.pdf 1 9B716059CB61470CDA9BD3377DBB0487 58f151f58dd0c360c08dde55672b026ecd274b6befa8926432deacc4aeaebe21 11e66689-7c10-11eb-bb7a-00155d0001ca 20.500.12556/dkum/f8b26ca0-9e73-47de-8875-c36ebdec5c00 https://dk.um.si/Dokument.php?lang=slv&id=126140 Fakulteta za naravoslovje in matematiko 0 0 0