Hello, (I searched the wohole literature and internet and I have no idea myself for this important question)

Let $(X_1,X_2)$ be a multivariate normal random vector ($X_1$ and $X_2$ need not be independent). Is it possible to calculate $$VaR_{\alpha}\bigl(e^{X_1}+e^{X_2}\bigr)$$ analyticaly? Or is it even possible to calulate it in terms of $$VaR_{\alpha}(e^{X_1}) \ \text{ and} \ VaR_{\alpha}(e^{X_2}),$$ i.e. is there a representation (a function $g(\cdot,\cdot)$) of the form $$VaR_{\alpha}(e^{X_1}+e^{X_2})=g\Bigl(VaR_{\alpha}\bigl(e^{X_1}\bigr),VaR_{\alpha}\bigl(e^{X_2}\bigr)\Bigr)$$.

I would be very thakful for hints.