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master's thesis
Poissonov proces i subordinatori
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:677329
Martinić, Miko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Martinić, M. (2015). Poissonov proces i subordinatori (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:677329

Martinić, Miko. "Poissonov proces i subordinatori." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:677329

Martinić, Miko. "Poissonov proces i subordinatori." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:677329

Martinić, M. (2015). 'Poissonov proces i subordinatori', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:677329

Martinić M. Poissonov proces i subordinatori [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:677329

M. Martinić, "Poissonov proces i subordinatori", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:677329

Metadata
TitlePoissonov proces i subordinatori
AuthorMiko Martinić
MentorBojan Basrak (mentor)
Committee memberBojan Basrak (predsjednik povjerenstva)
Committee memberNikola Sarapa (član povjerenstva)
Committee memberSaša Singer (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj diplomskog rada je opisati pojam subordinatora te prikazati osnovne primjere i primjenu subordinatora. Kako bismo mogli opisati teoriju subordinatora, morali smo opširno definirati dio teorije Lévyjevih procesa i Poissonovu točkovnu mjeru. Poissonovu točkovnu mjeru uvodimo kako bi prikazali subordinator kao proces koji odgovara intuitivno složenom Poissonovom procesu s linearnim pomakom. U radu smo opisali svojstva slike subordinatora te prikazali asimptotsko ponašanje puteva pomoću Dynkin-Lampertijevog teorema. Na kraju, kao primjer primjene subordinatora, definiramo teoriju rizika te dajemo primjer direktne primjene subordinatora u osiguranju opisujući složeni Poissonov model (poznatiji kao Crámer-Lundbergov model u aktuarskom kontekstu).
Abstract (english)
The main goal of this thesis is to define and present basics examples and application of subordinators. In order to describe the theory of subordinators, theory of Lévy processes and Poisson random measures are discussed first. We introduce Poisson random measure in order to present subordinator as a process that correspond essentially to compound Poisson process with linear drift. We describe characteristics of the range of subordinator and show asymptotic behaviour of its paths using Dynkin-Lamperti theorem. In the last chapter, to present applications, we define ruin probability and usage of subordinator in insurance by describing compound Poisson model (known as Crámer-Lundberg model in actuarial contest).
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:677329
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-23 11:14:06