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.

中文翻译：

---

持有轻尾物品投资组合的个体代理商网络的财务风险衡量

我们调查了一个代理商网络，该代理商网络持有独立轻尾风险对象投资组合，其损失以明显的尾部参数渐近指数分布。我们证明了投资组合损失的渐近分布属于本文介绍的函数指数混合的一类。我们还提供了风险价值和预期的短缺风险度量以及有条件的对应度量的结果。与重尾设置相比，我们在轻尾假设下在投资组合风险的渐近行为中建立了重要的定性差异，这在实际风险管理中必须加以考虑。