Financial risk measures for a network of individual agents holding portfolios of light-tailed objects

We investigate a financial network of agents holding portfolios of independent light-tailed risky objects whose losses are asymptotically exponentially distributed with distinct tail parameters. We show that the asymptotic distributions of portfolio losses belong to the class of functional exponential mixtures which we introduce in this paper. We also provide results for value-at-risk and expected shortfall risk measures, as well as for their conditional counterparts. Compared to heavy-tail settings, we establish important qualitative differences in the asymptotic behaviour of portfolio risks under a light-tail assumption which have to be accounted for in practical risk management.