Distortion risk measures, bounds for risk measures with a concave distortion function and their use in portfolio optimizationZdravkovska, Angela (Avtor) Košir, Tomaž (Mentor) risk measuresdistortion risk measuresportfolio optimizationThis 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.20252025-07-02 15:28:37Magistrsko delo/naloga170229sl