Conditional Value-at-Risk UnderEllipsoidal Uncertainties

Although Value-at-Risk (VaR) has been widely adapted in financial management, Conditional Value-at-risk (CVaR), which is also known as mean excess loss, mean shortfall, or tail VaR, has also gained importance over the past decade. This is largely owing to the more appealing mathematical properties of the latter. Based on Rockafellar and Uryasev’s idea, we are going to look into the CVaR under an ellipsoidal distribution. With the ad-hoc primal-dual interior-point algorithm, we will also focus on the technique that minimizes the CVaR under the framework of portfolio selection.