多元极值理论及其在风险理论中的应用

项目名称： 多元极值理论及其在风险理论中的应用

项目编号： No.11301500

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 毛甜甜

作者单位： 中国科学技术大学

项目金额： 23万元

中文摘要： 在现代社会中，极端风险已是不可回避的话题。极值理论是目前预测极端事件发生的可能性最有效的方法之一，但多局限于一元情形，多元情形的应用比较有限。因此，有必要对多元极值理论及其在风险理论中的应用进行深入研究。 由于在极值风险的研究中，通常没有足够的数据来明晰极端风险的精确分布以及风险之间的相依结构，难以明晰极值风险的尾部性状。因此，建立适当的刻画极值风险尾部渐近性质尤为必要。故本项目的主要内容包括：基于谱测度研究多元极值分布相依结构的刻画；多元极值风险的相依结构和边际分布如何影响尾部性状；多元极值风险的聚合的尾概率及风险度量的二阶逼近；在隐正则变化的条件下研究多元极值风险的风险度量；从聚合风险追溯边际风险的性质。本项目的研究成果可望为管理者在风险管理方面提供可靠的理论依据，丰富和发展极值理论。

中文关键词： 多元正则变化；二阶正则变化；风险度量；极值理论；谱测度

英文摘要： In modern society, the extreme risk has been an inevitable topic. Extreme value theory is one of the most effective methods to predict the probability of extreme events, but mostly restricted to the circumstances which only involve univariate risk. Application to the situations which involve the multivariate risks is still limited. So, it is necessary to conduct in-depth research on multivariate extreme value theory and its application in risk theory. In the study of extreme risk, the frequency of extreme event is very small, which results in few samples of extreme events and that we usually do not have enough data to clear the precise distribution of the extreme risk and the dependence structure between risks. Therefore, it is difficult to figure out the tail traits of multivariate extreme risks. So, it is particularly important to develop appropriate convergence theorems which characterize the approximation of the tail traits. The main contents of our project include: investigating the characterization of dependence structure of multivariate extreme risks based on spectral measure; how the dependence structure and margins of multivariate extreme risk affect its tail traits; the second-order asymptotic approximation of tail probabilities and risk measure of the aggregation of multivariate extreme risk; investi

英文关键词： Multivariate regular variation；Second-order regular variation；Risk measure；Extreme value theory；Spectral measure