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master's thesis
Potpunost modela financijskog tržišta u diskretnom vremenu
2016. urn:nbn:hr:126:164980
Varga, Marija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Cite this document

Varga, M. (2016). Potpunost modela financijskog tržišta u diskretnom vremenu (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:164980

Varga, Marija. "Potpunost modela financijskog tržišta u diskretnom vremenu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:164980

Varga, Marija. "Potpunost modela financijskog tržišta u diskretnom vremenu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:164980

Varga, M. (2016). 'Potpunost modela financijskog tržišta u diskretnom vremenu', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 07 September 2024, https://urn.nsk.hr/urn:nbn:hr:126:164980

Varga M. Potpunost modela financijskog tržišta u diskretnom vremenu [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2024 September 07] Available at: https://urn.nsk.hr/urn:nbn:hr:126:164980

M. Varga, "Potpunost modela financijskog tržišta u diskretnom vremenu", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:164980

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Metadata
TitlePotpunost modela financijskog tržišta u diskretnom vremenu
Title (english)Completeness of Financial Market Discrete Time Models
AuthorMarija Varga
MentorNenad Šuvak (mentor)
Committee memberDarija Marković (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2016-10-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Abstract
U ovom diplomskom radu cilj nam je bio analizirati potpunost modela financijskog tržišta u diskretnom vremenu. Kako bismo uopće mogli definirati potpunost matematičkog modela financijskog tržišta u diskretnom vremenu, prvo smo opisati financijsko tržište u diskretnom vremenu, financijske instrumente (osnovne i izvedene) kojima se trguje na financijskom trži- štu, te njihove cijene i povrate. Pritom smo od važnijih pojmova definirali pojmove kao što su portfelj, europska call i put opcija, samofinancirajuća i dopustiva strategija trgovanja, vjerojatnost neutralna na rizik, te arbitraža i martingal. Zatim smo opisali neke jednoperiodne i višeperiodne modele u diskretnom vremenu, koji koriste dva financijska instrumenta, od kojih je jedan nerizičan (novac u domaćoj valuti), a drugi rizičan (dionica). Nakon toga definirali smo slučajni zahtjev, te što treba biti zadovoljeno da bi taj slučajni zhatjev bio dostižan. Na temelju dobivenih rezultata definirali smo potpun model financijskog tržišta u diskretnom vremenu kao model tržišta bez arbitraže na kojemu je svaki slučajni zahtjev dostižan. Za svaki opisani model iznijeli smo neke zahtjeve koje ti modeli trebaju ispunjavati da bi bili potpuni.
Abstract (english)
This thesis aim was to analyse the completeness of financial market discrete time models. In order to even be able to define the completeness of financial market discrete time models, we first described the financial market in discrete time, financial instruments (basic and derived) that are traded on financial markets, and its prices and returns. In doing so, we of the important terms defined terms such as the portfolio, a European call and put options, self-financing and admissible trading strategy, the risk-neutral measure, arbitrage and martingale. Then we described some one-period and multi-period models in discrete time, using two financial instruments, one of which is risk free (money in local currency), and the other risk (stocks). Then we defined a contingent claim, and what needs to be satisfied that this contingent claim was admissible. Based on the obtained results, we have defined a complete model of the fi- nancial market in discrete time as a model market without arbitrage in which each contingent claim is admissible. For each described model we have put forward some demands that these models must fulfill in order to be complete.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:164980
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
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 on2016-11-02 07:23:11