VaR and ES for linear Portfolios with mixture of elliptically distributed Risk Factors

The particular subject of this paper, is to give an explicit formulas that will permit to obtain the linear VaR or Linear ES, when the joint risk factors of the Linear portfolios, changes with mixture of t-Student distributions. Note that, since one shortcoming of the multivariate t- distribution is that all the marginal distributions must have the same degrees of freedom, which implies that all risk factors have equally heavy tails, the mixture of t-Student will be view as a serious alternatives, to a simple t-Student-distribution. Therefore, the methodology proposes by this paper seem to be interesting to controlled thicker tails than the standard Student distribution.