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master's thesis
Skaliranje vremena u slučajnim procesima
2023. urn:nbn:hr:126:963631
Majdenić, Ivana
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Majdenić, I. (2023). Skaliranje vremena u slučajnim procesima (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:963631

Majdenić, Ivana. "Skaliranje vremena u slučajnim procesima." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:963631

Majdenić, Ivana. "Skaliranje vremena u slučajnim procesima." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:963631

Majdenić, I. (2023). 'Skaliranje vremena u slučajnim procesima', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:963631

Majdenić I. Skaliranje vremena u slučajnim procesima [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:963631

I. Majdenić, "Skaliranje vremena u slučajnim procesima", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:963631

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Metadata
TitleSkaliranje vremena u slučajnim procesima
Title (english)Time-Changed Stochastic Processes
AuthorIvana Majdenić
MentorNenad Šuvak (mentor)
Committee memberDanijel Grahovac (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-10-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Financial and Business Mathematics
Abstract
U ovom diplomskom radu bavimo se skaliranjem vremena u slučajnim procesima. Definiramo proces skaliranja vremena, te promatramo skaliranje vremena u difuzijama i Black-Scholes-Mertonovom modelu. Pomoću rezultata navedenih u poglavlju skaliranje vremena u difuzijama dokazujemo rezultate potrebne za izvod Black-Scholes-Mertonove formule za određivanje nearbitražne cijene europske call opcije. Nadalje, definiramo frakcionalnu difuzije pomoću Pearsonove difuzije u kojoj vrijeme modeliramo inverzom stabilnog subordinatora. Na kraju rada simuliramo trajektorije frakcionalne recipročne gama i Fisher-Snedecorove difuzije.
Abstract (english)
In this thesis, we deal with time-changed stohastic processes. We define the change of time process and observe time change in diffusions and the Black-Scholes-Merton model. Using the results given in the chapter time change in diffusions, we prove the results necessary for the derivation of the Black-Scholes-Merton formula for determining the non-arbitrage price of the European call option. Furthermore, we define fractional diffusion using Pearson diffusion in which time is modeled by the inverse of a stable subordinator. At the end of the thesis, we simulate the trajectories of fractional reciprocal gamma and Fisher-Snedecor diffusion.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:963631
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 on2023-11-07 10:11:59