Computing the portfolio Conditional Value-at-Risk in the Alfa-stable case

The class of stable distributions is attractive as a probabilistic model of asset returns distribution in the field of finance. In many practical problems, such as optimal portfolio selection, it is important that we are able to compute accurately the Conditional Value-at-Risk (CVaR), also known as expected tail loss (ETL), which is proposed in the literature as a coherent measure of risk. The paper proposes an integral expression for the calculation of the CVaR and compares the current approach to some existing methods. We demonstrate how to relate the derived result to some common multivariate distributional assumptions.