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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

Institutional repository: Repository of the Faculty of Science

Cite this document

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

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

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

Lehman Pavasović, K. (2022). 'Metode neglatke optimizacije u teoriji portfelja', Master's thesis, University of Zagreb, Faculty of Science, accessed 01 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:772421

Lehman Pavasović K. Metode neglatke optimizacije u teoriji portfelja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 June 01] Available at: https://urn.nsk.hr/urn:nbn:hr:217:772421

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

Metadata
TitleMetode neglatke optimizacije u teoriji portfelja
Title (english)Methods of non-smooth optimization in portfolio theory
AuthorKatarina Lehman Pavasović
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberHrvoje Planinić (član povjerenstva)
Committee memberAna Prlić (član povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-12-01, 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)
Languagecroatian
URN:NBNurn:nbn:hr:217:772421
Study programmeTitle: Finance and Business 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 on2022-12-16 13:33:11