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master's thesis
Koherentne mjere rizika
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:483549
Fioretti, Lucija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Fioretti, L. (2020). Koherentne mjere rizika (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:483549

Fioretti, Lucija. "Koherentne mjere rizika." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:483549

Fioretti, Lucija. "Koherentne mjere rizika." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:483549

Fioretti, L. (2020). 'Koherentne mjere rizika', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:483549

Fioretti L. Koherentne mjere rizika [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:483549

L. Fioretti, "Koherentne mjere rizika", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:483549

Metadata
TitleKoherentne mjere rizika
AuthorLucija Fioretti
MentorMiljenko Huzak (mentor)
Committee memberMiljenko Huzak (predsjednik povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu diskutiramo poželjna svojstva mjera rizika, te mjeru koja zadovoljava određena svojstva nazivamo "koherentnom". Aksiomatski definiramo "prihvatljive" skupove te pokazujemo njihovu vezu sa koherentnim mjerama rizika. Nadalje, pokazujemo reprezentaciju koherentnih mjera rizika uz pomoć generaliziranih scenarija. Na kraju proučavamo tri konkretne mjere rizika: Value-at-Risk, najgore uvjetno očekivanje i očekivani manjak. Pokazujemo da Value-at-Risk, unatoč tome što je široko primijenjena, nije koherentna te ukazujemo na potencijalne probleme primjene takve mjere. Najgore uvjetno očekivanje dajemo kao koherentnu mjera rizika od teoretskog značaja, a očekivani manjak predlažemo kao koherentnu alternativu praktične primjene.
Abstract (english)
In this paper, we discuss desirable properties for measures of risk, and call the measure satisfying appropriate properties "coherent". We deffine by axioms "acceptable" sets, and show their relation to coherent risk measures. Furthermore, we give the representation of coherent risk measures in terms of generalized scenarios. In the end, we study three measures of risk: Value-at-Risk, the worst conditional expectation and expected shortfall. We show that Value-at-Risk, despite being widely used, isn't coherent and we point out potential problems in that regard. We give the worst conditional expectation as a coherent risk measure of theoretical importance, while we propose expected shortfall as a coherent alternative of practical usage.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:483549
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 on2020-12-10 13:34:09