Zaraza u financijskim mrežama

master's thesis

• Author: Tena Zbiljski
• Mentor: Boris Podobnik (mentor)
• Committee member: Boris Podobnik (predsjednik povjerenstva)
• Committee member: Luka Grubišić (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kroz povijest smo svjedoci nekoliko većih slomova financijskog sustava pa se postavlja pitanje njihovog uzroka. Iako pojmu ”financijski sustav” pripada niz različitih posrednika, kako bi se olakšala terminologija, u ovom radu se govori o međubankovnom sustavu koji je sačinjen od n banaka i njihovih međusobnih potraživanja. Rad obrađuje temu zaraze u financijskim mrežama - vjerojatnosti nastanka i opseg širenja ukoliko do nje dođe. Pojam zaraza je izjednačen sa bankrotom banke koji se prenosi s jedne na drugu. Teorijski dio modela zasniva se na usmjerenom grafu i funkcijama izvodnicama koje generiraju vjerojatnosnu distribuciju stupnjeva vrhova, dok se u drugom djelu rada prikazuju rezultati koji potvrđuju teorijske pretpostavke. Zaključuje se da postoji ”prozor” u kojem do zaraze dolazi za određene vrijednosti stupnjeva vrhova u grafu. Iako sustav može biti otporan na većinu šokova neke jakosti, ako je pogođen takvim šokom na specifičnom mjestu, koje je možda strukturna slabost sustava, posljedična nestabilnost sustava može biti značajna. Pokazuje se da je financijski sustav robustan, ali krhak - iako je vjerojatnost zaraze mala, njezine posljedice mogu biti ekstremno proširene.

Abstract (english)

Throughout history we have witnessed several major breakdowns of the financial system which leads to the question of their causes. Although to the term ”financial system” belongs a variety of intermediaries, to facilitate terminology, this paper discusses the interbank system, which is made up of n banks and their mutual claims to each other. The paper discusses the contagion in financial networks - the probability of occurrence and the extent of its spread, if it occurs. The term contagion is equated with bankruptcy of banks which is transferred from one bank to another. The theoretical part of the model is based on a directed graph and generating functions that generate a probability degree distribution, while the second part of the paper presents results that confirm the theoretical assumptions. The conclusion is that there is a ”window” in which infection breaks out for a certain value of average degree in the graph. Although the system can be resistant to most shocks of particular magnitude, if it is hit by such a shock to a specific place, which may have been structural weakness of the system, the instability of the system can be significant. It turns out that the financial system is robust, but fragile - although the probability of contagion is low, the consequences can be extremely widespread.

• Keywords: slom financijskog sustava; međubankovnom sustav; zaraze u financijskim mrežama; bankrot; usmjereni graf
• Keywords (english): breakdown of the financial system; interbank system; contagion in financial networks; bankruptcy; directed graph
• Language: croatian
• URN:NBN: urn:nbn:hr:217:496223
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-20 12:01:48