Koherentne mjere rizika

master's thesis

• Author: Lucija Fioretti
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, 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: Value-at-Risk; najgore uvjetno očekivanje; očekivani manjak
• Keywords (english): measures of risk; Value-at-Risk; the worst conditional expectation; expected shortfall
• Language: croatian
• URN:NBN: urn:nbn:hr:217:483549
• 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
• Created on: 2020-12-10 13:34:09