Mere tveganja, invariantne za verjetnostne porazdelitve : delo diplomskega seminarja

Blagotinšek, Regina (author), Škulj, Damjan (mentor)

Diplomski seminar karakterizira koherentne mere tveganja, invariantne za verjetnostne porazdelitve. Mera tveganja je koherentna, če je monotona, translacijsko invariantna, subaditivna in pozitivno homogena. Če ima še lastnost invariantnost za verjetnostne porazdelitve, slučajnim spremenljivkam, ki so enako porazdeljene, priredi enako vrednost. Mere tveganja, invariantne za verjetnostne porazdelitve, so pomembno orodje pri merjenju in obvladovanju tveganja na finančnem področju. Pri vrednotenju tveganja lahko upoštevamo tudi posameznikove preference o tveganju, in sicer z uporabo mer spektralnega tveganja. V praksi je verjetnostna porazdelitev težko določljiva, in da upoštevamo to negotovost porazdelitve, lahko uporabimo mere tveganja za najslabši primer, ki določijo najvišjo možno stopnjo tveganja.

• Language: Slovenian
• Keywords: mera tveganja, koherentnost, invariantnost za verjetnostne porazdelitve, Fatoujeva lastnost, mera tvegane vrednosti, mera spektralnega tveganja, mera tveganja za najslabši primer
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-148108
• UDC: 519.8
• COBISS.SI-ID: 159891459
• Publication date in RUL: 27.07.2023

BLAGOTINŠEK, Regina, 2023, Mere tveganja, invariantne za verjetnostne porazdelitve : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 3 June 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=148108

Secondary language

• Language: English
• Title: On law invariant risk measures

Abstract

The seminar characterizes on law invariant coherent risk measures. A risk measure is coherent if it is monotone, translationally invariant, subadditive and positively homogeneous. If it is also law invariant, it assigns the same value to random variables that are identically distributed. Law invariant coherent risk measures are an important tool for measuring and managing risk in the financial sector. In risk assessment, we can also consider individual's risk preferences by using spectral risk measures. In most cases, it is difficult to determine the probability distribution. To avoid this uncertainty in the distribution, we can use worst case risk measures that determine the highest possible level of risk.

• Keywords: risk measure, coherence, law invariance, Fatou property, Value-at- Risk, spectral risk measure, worst-case risk measure