Before revision: In this paper, we introduce a multivariate extension of the classical univariate Value-at-Risk (VaR)  . This extension may be useful to understand how solvency capital requirement is affected by the presence of risks that cannot be diversify away. This is typically the case for a network of highly interconnected financial institutions in a macro-prudential regulatory system. We also generalize the bivariate Conditional-Tail-Expectation (CTE), previously introduced by Di Bern- ardino et al. (2011), in a multivariate setting and we study its behavior.
After revision: In this paper, we introduce a multivariate extension of the classical univariate Value-at-Risk (VaR) .