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.
After revision: In this paper, we introduce a multivariate extension 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 portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level sets of multivariate survival functions . This extension may be useful to understand how solvency capital requirement is affected by the presence of risks that cannot be diversify away.