Computing the Portfolio Conditional Value-at-Risk in the Alpha-Stable Case

The class of alpha-stable distributions is an attractive probabilistic model of asset returns distribution in the field of finance. When dealing with real issues, such as optimal portfolio selection, it is important that we can compute the Conditional Value-at-Risk (CVaR) accurately. CVaR is also known as expected tail loss (ETL) proposed in the literature as a coherent risk measure. In our paper, we propose an integral expression for the calculation of the CVaR of a stable law. We compare the current approach to some existing methods and we demonstrate how to relate the derived result to some common multivariate distributional assumptions