20.500.12556/RUL-170229 Distortion risk measures, bounds for risk measures with a concave distortion function and their use in portfolio optimization magistrsko delo Distorzijske mere tveganja, meje za mere tveganja s konkavno distorzijsko funkcijo in njihova uporaba pri optimizaciji portfeljev This master's thesis studies distortion risk measures, a class of risk measures which are more flexible in reflecting decision-makers' preferences under risk and uncertainty. Distortion risk measures were derived from decision theory, particularly the dual theory of choice under risk proposed by Yaari in 1987, and have since gained recognition increasingly due to the limitations of classical risk measures such as the mathematical expectation which does not account for variability, and value at risk (VaR) which fails to capture tail risk and in general does not support diversification, same as the standard deviation. Distortion risk measures are defined through the transformation of the underlying probability distribution using a distortion function, which can be chosen so that the risk measure possesses desired properties. In fact, a key result reviewed is that a concave distortion function yields a coherent risk measure. Recent results on bounds for concave distortion risk measures show that they can be used in a robust portfolio optimization problem, where the true distribution is subject to uncertainty. Using the results on worst-case value bounds for distortion risk measures, this thesis demonstrates their practical relevance by calculating the optimal portfolio using data from Yahoo Finance. Ta magistrska naloga proučuje distorzijske mere tveganja, razred mer tveganja, ki omogočajo večjo prilagodljivost pri upoštevanju preferenc odločevalcev v pogojih tveganja in negotovosti. Distorzijske mere tveganja izvirajo iz teorije odločanja, natančneje iz dualne teorije odločanja v razmerah tveganja, ki jo je leta 1987 predlagal Yaari. V zadnjih desetletjih so te mere pridobile na veljavi, predvsem zaradi pomanjkljivosti klasičnih mer tveganja, kot je matematično upanje, ki ne upošteva variabilnosti, ter tvegana vrednost (VaR), ki ne zajema tveganja repa porazdelitve in praviloma ne podpira diverzifikacije, podobno kot standardni odklon. Distorzijske mere tveganja so definirane s transformacijo osnovne verjetnostne porazdelitve s pomočjo distorzijske funkcije, ki jo je mogoče izbrati tako, da ima mera tveganja želene lastnosti. Eden ključen rezultat, obravnavan v nalogi, je, da konkavna distorzijska funkcija zagotavlja koherentnost mere tveganja. Nedavni rezultati o mejah konkavnih distorzijskih mer tveganja kažejo, da jih je mogoče uporabiti tudi pri robustni optimizaciji portfelja, kjer je resnična porazdelitev verjetnosti podvržena negotovosti. Na podlagi rezultatov o najslabšem možnem scenariju za vrednost distorzijskih mer tveganja v nalogi prikažemo njihovo praktično uporabnost z izračunom optimalnega portfelja na podatkih s platforme Yahoo Finance. risk measures distortion risk measures portfolio optimization mere tveganja distorzijske mere tveganja optimizacija portfeljev true false false Angleški jezik Slovenski jezik Magistrsko delo/naloga 2025-07-02 15:28:37 2025-07-02 15:28:39 2025-07-07 13:01:03 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 150690 239617795 17938.pdf 17938.pdf 1 C9BB5E1ABE081E43DA9795F5D73FC4C5 4a6d1e5e805c7a7f45c3573730d0475bcab8f08975d2450d16f01d6abcdddb6d 9588a941-5746-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=212187 17939.ipynb 17939.ipynb 1 453D885FB8E847D5295A83FCCE200D83 55b891fe08931d9b6372a5d540b317f4f18f5e856c2f27ed9d7ee438e67821f9 95896cf4-5746-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=212188 Fakulteta za matematiko in fiziko 0 0 0