Aproksimativna master jednadžba i njena upotreba u kontaktnim procesima

master's thesis

• Title (english): Approximate master equation and its application in contact processes
• Author: Marko Bandalo
• Mentor: Vinko Zlatić (mentor)
• Mentor: Denis Sunko (komentor)
• Committee member: Denis Sunko (predsjednik povjerenstva)
• Committee member: Vinko Zlatić (član povjerenstva)
• Committee member: Miroslav Požek (član povjerenstva)
• Committee member: Damjan Pelc (član povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-09-30, 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: kompleksne mreže; sistematski rizici; aproksimativna master jednadžba
• Language: croatian
• URN:NBN: urn:nbn:hr:217:892344
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2023-09-30
• Created on: 2022-10-20 12:31:03