underlying risk portfolio. As for the multivariate Value-at-Risk measures introduced by Cousin and Di Bernardino (2013), the …. of multivariate survival distribution functions). Contrary to allocation measures or systemic risk measures, these … measures are also suitable for multivariate risk problems where risks are heterogeneous in nature and cannot be aggregated …

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a … multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk …, we show that both these risk measures satisfy the positive homogeneity and the translation invariance property …

) in a multivariate setting. Contrary to allocation measures or systemic risk measures, these measures are also suitable … for multivariate risk problems where risks are heterogenous in nature and cannot be aggregated together. …

CoVaR is a systemic risk measure proposed by Adrian and Brunnermeier (2011) able to measure a financial institution …’s contribution to systemic risk and its contribution to the risk of other financial institutions. CoVaR stands for conditional Value-at-Risk …, i.e. it indicates the Value at Risk for a financial institution that is conditional on a certain scenario. In this paper …

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a … multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk …, we show that these risk measures both satisfy the positive homogeneity and the translation invariance property …

the stochastic order typically used in the univariate case. These utility functions are multivariate risk averse, and … risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare …