Metode najgoreg slučaja u teoriji portfelja

master's thesis

• Title (english): Worst case methods in portfolio theory
• Author: Anđela Jurišić
• Mentor: Marko Vrdoljak (mentor)
• Committee member: Marko Vrdoljak (predsjednik povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-07-19, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog rada bio je prikazati metodu najgoreg slučaja u teoriji portfelja. Uveli smo teorijsku podlogu potrebnu za razumijevanje zadaće optimizacije portfelja te promatrali optimizaciju portfelja u kontekstu metode najgoreg slučaja, konkretno mjere \(l_{\infty}\). U prvom poglavlju definirali smo mjere rizika \(l_{\infty}\) i alternativnu \(l_{\infty}\). Pretpostavljajući da kratka prodaja nije dozvoljena, izveli smo eksplicitno rješenje i analizirali optimalnu investicijsku strategiju za učinkovitu granicu problema optimizacije portfelja. Optimalnost rješenja osigurana je pomoću Karush-Kuhn-Tuckerovih uvjeta. U trećem poglavlju analizirali smo ukupni rizik portfelja te usporedili model \(l_{\infty}\) i model srednje varijance kojeg je uveo Markowitz.

Abstract (english)

The aim of this paper was to present the worst-case method in portfolio theory. We provided the necessary theoretical background for understanding portfolio optimization and focused on portfolio optimization using the worst-case method, specifically the \(l_{\infty}\) risk measure. In the first chapter, we defined the \(l_{\infty}$ and the alternative \(l_{\infty}\) risk measures. Assuming the absence of short selling, we derived an explicit solution and analyzed the optimal investment strategy for the efficient frontier of the portfolio optimization problem. The optimality of the solution was ensured through the Karush-Kuhn-Tucker conditions. In the third chapter, we analyzed the overall portfolio risk and compared the \(l_{\infty}\) model with the mean-variance model introduced by Markowitz.

• Keywords: optimizacija portfelja; mjere rizika; optimalna investicijska strategija; Karush-Kuhn-Tuckerovi uvjeti; Markowitz
• Language: croatian
• URN:NBN: urn:nbn:hr:217:543825
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-08 16:29:13