英文标题：
《Tail probabilities of random linear functions of regularly varying
random vectors》
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作者：
Bikramjit Das, Vicky Fasen-Hartmann and Claudia Kl\\\"uppelberg
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最新提交年份：
2020
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英文摘要：
We provide a new extension of Breiman\'s Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\\infty)^d$ under random linear transformations. This allows us to compute probabilities of a variety of tail events, which classical multivariate regularly varying models would report to be asymptotically negligible. We illustrate our findings with applications to risk assessment in financial systems and reinsurance markets under a bipartite network structure.
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中文摘要：
我们提供了一个新的扩展布雷曼定理计算尾部概率的乘积随机变量的多元设置。特别地，我们给出了锥上正则变化的一个完整刻划$随机线性变换下的概率为[0，infty）^d$。这使我们能够计算各种尾部事件的概率，而经典的多变量规则变化模型将报告为渐近可忽略不计。我们通过将我们的发现应用于二部网络结构下金融系统和再保险市场的风险评估来说明我们的发现。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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