Metode neglatke optimizacije u teoriji portfelja

Lehman Pavasović, Katarina

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master's thesis

Metode neglatke optimizacije u teoriji portfelja

Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:772421

Lehman Pavasović, Katarina

University of Zagreb
Faculty of Science
Department of Mathematics

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APA 6th Edition

Lehman Pavasović, K. (2022). Metode neglatke optimizacije u teoriji portfelja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:772421

MLA 8th Edition

Lehman Pavasović, Katarina. "Metode neglatke optimizacije u teoriji portfelja." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:772421

Chicago 17th Edition

Lehman Pavasović, Katarina. "Metode neglatke optimizacije u teoriji portfelja." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:772421

Harvard

Lehman Pavasović, K. (2022). 'Metode neglatke optimizacije u teoriji portfelja', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:772421

Vancouver

Lehman Pavasović K. Metode neglatke optimizacije u teoriji portfelja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2025 January 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:772421

IEEE

K. Lehman Pavasović, "Metode neglatke optimizacije u teoriji portfelja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:772421

Cite this item: https://urn.nsk.hr/urn:nbn:hr:217:772421

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Metadata

Title	Metode neglatke optimizacije u teoriji portfelja
Title (english)	Methods of non-smooth optimization in portfolio theory
Author	Katarina Lehman Pavasović
Mentor	Marko Vrdoljak (mentor)
Committee member	Marko Vrdoljak (predsjednik povjerenstva)
Committee member	Hrvoje Planinić (član povjerenstva)
Committee member	Ana Prlić (član povjerenstva)
Committee member	Siniša Slijepčević (član povjerenstva)
Granter	University of Zagreb Faculty of Science (Department of Mathematics) Zagreb
Defense date and country	2022-12-01, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics
Abstract	Cilj ovog rada bio je prikazati primjenu neglatke optimizacije u teoriji portfelja. Najprije smo dali pregled teorije koja je vezana uz povrate portfelja, njihove distribucije, učinkovitost i rizičnost. Nakon toga smo prikazali najpoznatije mjere rizika koje se koriste u optimizaciji portfelja te sugerirali korištenje mjere CVaR jer je koherentna i može se koristiti u situacijama kada gubici nisu normalno distribuirani. U drugome poglavlju prikazali smo model optimizacije portfelja u kontekstu mjere rizika CVaR. Budući da izraz za CVaR sadrži funkciju \(x^+=\max (0,x) \), to je problem neglatke optimizacije. Rješavanju problema moguće je pristupiti na dva načina: transformirati zadaću u problem linearnog programiranja ili direktno riješiti zadaću pogodnom metodom neglatke optimizacije. U radu smo predstavili oba načina, uz poseban naglasak na direktnu primjenu diskretne gradijentne metode. Takav pristup daje učinkovitije rješenje, pogotovo u situacijama kada želimo pronaći optimalne portfelje, a promatramo veliki broj scenarija.
Abstract (english)	The aim of this thesis was to show application of non-smooth optimization in portfolio theory. First we gave an overview on theory which is related to portfolio returns, distribution of returns, efficiency and riskiness. After that we introduced the most popular risk measures in portfolio optimization and suggested use of CVaR because it is coherent and it can be used even if distribution of returns is not normal. In the second chapter we described portfolio optimization model in the context of CVaR measure. Since expression for CVaR contains a function \(x^+=\max (0,x) \), it is a non-smooth optimization problem. To solve this problem, one could use two ways: transform the problem into a linear programming model or directly solve the problem using an appropriate non-smooth method. In this thesis we introduced both ways, with special emphasis on direct application of discrete gradient method. Such approach gives a more efficient solution, especially when we want to find optimal solution for portfolios with large number of scenarios.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:217:772421
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
Terms of use
Repository	Repository of the Faculty of Science
Created on	2022-12-16 13:33:11