Properties and calculation of multivariate risk measures: MVaR and MCVaR

A recent paper by Prékopa (Ann. Oper. Res. 193(1):49–69, 2012) presented results in connection with Multivariate Value‐at‐Risk (MVaR) that has been known for some time under the name of p‐quantile or p‐Level Efficient Point (pLEP) and introduced a new multivariate risk measure, called Multivariate Conditional Value‐at‐Risk (MCVaR). The purpose of this paper is to further develop the theory and methodology of MVaR and MCVaR. This includes new methods to numerically calculate MCVaR, for both continuous and discrete distributions. Numerical examples with recent financial market data are presented.