Ekvilibrij u financijskoj teoriji u diskretnom vremenu

master's thesis

• Author: Stela Svažić
• Mentor: Hrvoje Šikić (mentor)
• Committee member: Hrvoje Šikić (predsjednik povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Committee member: Saša Singer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-03-06, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu pokazali smo osnovne rezultate egzistencije ekvilibrija u financijskoj teoriji u diskretnom vremenu. Započeli smo uvođenjem matematičkih definicija i rezultata s financijskom interpretacijom. Zatim smo postavili uvjete poput nepostojanja arbitraže i svojstava funkcija korisnosti te uveli agregatnu funkciju viška potražnje na temelju čega smo razvili teoriju i dokazali egzistenciju ekvilibrija. Ekvilibrij smo povezali s efikasnošću pomoću Pareto optimalnosti. Slijedili smo Arrowovu ideju uvođenja financijskih tržišta te tako iskazivali rezultate egzistencije ekvilibrija za pojedine slučajeve tržišta i na temelju njih izvodili zaključke. Na kraju, izveli smo poznatu beta jednadžbu CAPM modela koji je danas često u uporabi.

Abstract (english)

In this study we proved the fundamental results of equilibrium in financial theory in discrete time. We started by introducing mathematical definitions and results with financial interpretation. Then we set conditions such as non-arbitrage, characteristics of utility functions and introduced the aggregate excess demand function that helped us develop the theory and prove the existence of the equilibrium. Pareto optimal allocation helped us link the equilibrium to efficiency. We followed Arrow’s idea of introducing financial markets, subsequently showing the results of equilibrium existence on certain market cases and according to them made conclusions. In the end, we derived the well-known beta equation through the Capital Asset Princing Model which is commonly used today.

• Keywords: egzistencija ekvilibrija; financijska teorija; diskretno vrijeme; arbitraža; Pareto optimalnost; CAPM model
• Keywords (english): equilibrium; financial theory; discrete time; arbitrage; Pareto optimal allocation; Capital Asset Princing Model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:477356
• 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: 2020-10-07 09:52:00