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master's thesis
Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:892344
Bandalo, Marko
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

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Bandalo, M. (2022). Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:892344

Bandalo, Marko. "Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:892344

Bandalo, Marko. "Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:892344

Bandalo, M. (2022). 'Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima', Master's thesis, University of Zagreb, Faculty of Science, accessed 31 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:892344

Bandalo M. Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 31] Available at: https://urn.nsk.hr/urn:nbn:hr:217:892344

M. Bandalo, "Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:892344

Metadata
TitleAproksimativna master jednadžba i njena upotreba u kontaktnim procesima
Title (english)Approximate master equation and its application in contact processes
AuthorMarko Bandalo
MentorVinko Zlatić (mentor)
MentorDenis Sunko (komentor)
Committee memberDenis Sunko (predsjednik povjerenstva)
Committee memberVinko Zlatić (član povjerenstva)
Committee memberMiroslav Požek (član povjerenstva)
Committee memberDamjan Pelc (član povjerenstva)
Committee memberDanko Radić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2022-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Cilj ovog rada je, kroz različite modele promotriti širenje zaraze na kompleksnim mrežama te kasnije proširiti tu logiku na financijske sustave. Rad počinje s binarnom dinamikom na mrežama, poput SIS modela, koji se mogu opisati pomoću stopa tranzicije koje ovise o broju susjeda u jednom od dva moguća stanja. Dinamika će se aproksimirati s aproksimativnom master jednadžbom, aproksimacijom parova i aproksimacijom srednjeg polja, pa će se usporediti njihova rješenja. Zatim promatramo analitički model širenja zaraze na mreži. Istražuje se kako vjerojatnost i potencijalni utjecaj zaraze ovise o agregatnim i idiosinkratskim šokovima, promjenama u mrežnim strukturama i likvidnosti tržišta. Za kraj će se razviti model širenja zaraze, odnosno insolventnosti, u ovisnosti o kapitalu pojedine banke, te se usporediti s modelom praga.
Abstract (english)
The goal of this paper is to observe the spread of contagion on complex networks through different models and to extend this logic later to financial systems. The paper starts with binary dynamics on networks, such as the SIS model, which can be described by transition rates that depend on the number of neighbors in one of two possible states. The dynamics will be approximated with the approximate master equation, pair approximation and mean field approximation and their solutions will be compared. After that what will be observed is an analytical model of contagion in financial networks with arbitrary structure. The paper explores how the probability and potential impact of contagion are influenced by aggregate and idiosyncratic shocks, changes in network structure, and asset market liquidity. Finally, a model of the spread of contagion, i.e. insolvency, will be developed, depending on the capital of an individual bank, and that model will be compared with the threshold model.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:217:892344
Study programmeTitle: Physics; specializations in: Research
Course: Research
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Embargo expiration date: 2023-09-30
Terms of useLicence In copyright icon
Created on2022-10-20 12:31:03