In this talk we consider a financial network of agents holding portfolios of independent light-tailed risky objects with losses assumed to be asymptotically exponentially distributed with distinct tail parameters. The derived asymptotic distributions of portfolio losses refer to the class of functional exponential mixtures. We also provide statements for Value-at-Risk and Expected Shortfall measures as well as for their conditional counterparts. We establish important qualitative differences in the asymptotic behavior of portfolio risks under light tail assumption compared to heavy tail settings which should be accounted for in practical risk management. (joint work with Claudia Klüppelberg)