Abstract
This dissertation addresses the optimisation of a class of risk measures referred to as coherent
distortion risk measures (CDRMs) within the portfolio optimisation framework by leveraging
linear programming techniques. The research was built upon the Conditional-Value-at-Risk
(CVaR) methodology introduced by Rockafellar and Uryasev (2000) and extended Feng and
Tan (2012) by incorporating the GlueVaR risk measure that was first introduced by Belles-
Sampera et al. (2014a) into a broader Generalised GlueVaR framework. The study explored
a range of established risk measures within the CDRM family, including CVaR, the Wang
Transform (WT), the Proportional Hazard (PH), the Beta Transform (BT), and the Dual
Power Transform (DP) risk measures.
Empirical analyses and case studies were conducted to demonstrate the versatility of the
linear programming method for solving the CDRM optimisation problem. The dissertation
investigated how different CDRMs perform in real-world portfolio scenarios and provided insights
into their comparative effectiveness in managing risk. By focusing on coherent distortion
risk measures, the research highlighted their practical relevance for financial institutions
aiming to balance return and risk under varying market conditions. The findings reinforced
the significance of advanced risk measures in portfolio optimisation, particularly in achieving
better risk-adjusted returns.