Sestavljen Poissonov model

Šuligoj, Jernej

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Title:	Sestavljen Poissonov model
Authors:	ID Šuligoj, Jernej (Author) ID Benkovič, Dominik (Mentor) More about this mentor...
Files:	MAG_Suligoj_Jernej_2018.pdf (503,47 KB) MD5: 9B716059CB61470CDA9BD3377DBB0487 PID: 20.500.12556/dkum/f8b26ca0-9e73-47de-8875-c36ebdec5c00
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	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.
Keywords:	Poissonov proces, sestavljen Poissonov proces, zavarovalniˇstvo, verjetnost propada, ˇcas propada, Pollaczeck-Khinchinova formula
Place of publishing:	Maribor
Publisher:	[J. Šuligoj]
Year of publishing:	2018
PID:	20.500.12556/DKUM-71000
UDC:	368:519.22(043.2)
COBISS.SI-ID:	24023304
NUK URN:	URN:SI:UM:DK:PUQWLZ5B
Publication date in DKUM:	24.09.2018
Views:	1445
Downloads:	136
Metadata:
Categories:	FNM
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Licences

License:	CC BY-ND 4.0, Creative Commons Attribution-NoDerivatives 4.0 International

Link:	http://creativecommons.org/licenses/by-nd/4.0/
Description:	Under the NoDerivatives Creative Commons license one can take a work released under this license and re-distribute it, but it cannot be shared with others in adapted form, and credit must be provided to the author.
Licensing start date:	28.06.2018

Secondary language

Language:	English
Title:	The compound Poisson model
Abstract:	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.
Keywords:	Poisson process, compound Poisson process, ensurance, probability of ruin, time to ruin, Pollaczeck-Khinchine formula

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