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master's thesis
Matematika Ponzijeve sheme
2022. urn:nbn:hr:126:481880
Biuk, Vesna
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Biuk, V. (2022). Matematika Ponzijeve sheme (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:481880

Biuk, Vesna. "Matematika Ponzijeve sheme." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:481880

Biuk, Vesna. "Matematika Ponzijeve sheme." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:481880

Biuk, V. (2022). 'Matematika Ponzijeve sheme', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 11 April 2024, https://urn.nsk.hr/urn:nbn:hr:126:481880

Biuk V. Matematika Ponzijeve sheme [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 April 11] Available at: https://urn.nsk.hr/urn:nbn:hr:126:481880

V. Biuk, "Matematika Ponzijeve sheme", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:481880

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Metadata
TitleMatematika Ponzijeve sheme
Title (english)Mathematics of Ponzy Scheme
AuthorVesna Biuk
MentorNenad Šuvak (mentor)
Committee memberDanijel Grahovac (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-06-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Financial and Business Mathematics
Abstract
Tema ovog rada je Ponzijeva shema, jedan od najpoznatijih oblika investicijske prijevare. Glavni cilj rada je konstruiranje matematičkog modela Ponzijeve sheme pomoću kojega smo kasnije uspjeli doći do zaključaka o održivosti sheme. Model smo konstruirali koristeći linearnu diferencijalnu jendadžbu i ranije poznate podatke o originalnoj Ponzijevoj shemi. Konstruirani model ovisi o određenim parametrima te smo željeli saznati kako promjena vrijednosti tih parametara utječe na održivost sheme. U tu svrhu u Matlabu smo napravili grafičke simulacije modela za nekoliko različitih kombinacija parametara. Promatrajući grafičke simulacije došli smo do zaključka kako Ponzijeva shema može biti održiva neograničeno dugo samo ako je upravitelj fonda spreman uložiti veliki iznos početnog kapitala, no tada on ne bi ostvario nikakvu dobit. U suprotnom, ako upravitelj sheme želi ostvariti dobit, onda ´ce u odredenom trenutku doći do manjka novih investitora te će svaka takva shema biti osuđena na propast.
Abstract (english)
The topic of this paper is the Ponzi scheme, one of the most well-known forms of investment fraud. The main goal of this paper is to construct a mathematical model of the Ponzi scheme by which we later managed to draw conclusions about the viability of the scheme. We constructed the model by using linear differential equation and previously known data about the original Ponzi scheme. The constructed model depends on certain parameters, and we wanted to find out how changing the values of these parameters affects the viability of the scheme. For this purpose, we made graphical simulations of the model for several different combinations of parameters by using Matlab. By observing those graphical simulations, we concluded that the Ponzi scheme can be viable indefinitely only if the fund manager is willing to invest a large amount of initial capital, but then he would not make any profit. On the contrary, if the scheme manager wants to make a profit, then at some point there will be a shortage of new investors and any such scheme will be doomed to failure.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:481880
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 on2022-06-28 06:53:22