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摘要翻译：
本文引入随机序的新概念，比较了多变量随机风险模型与极端投资组合损失的关系。在多元正则变分框架下，根据谱测度的排序条件导出了比较判据，为实际应用中的解析或数值验证提供了依据。根据进一步的随机排序，导出了附加的比较准则。应用实例包括最坏情况和最佳情况情景，椭圆等高线分布，以及具有Gumbel、Archimedean和Galambos Copulas的多变量规则变化模型。
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英文标题：
《Ordering of multivariate probability distributions with respect to
extreme portfolio losses》
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作者：
Georg Mainik and Ludger R\"uschendorf
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最新提交年份：
2010
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分类信息：
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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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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英文摘要：
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical verification in practical applications. Additional comparison criteria in terms of further stochastic orderings are derived. The application examples include worst case and best case scenarios, elliptically contoured distributions, and multivariate regularly varying models with Gumbel, Archimedean, and Galambos copulas.
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PDF链接：
https://arxiv.org/pdf/1010.5171
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