# 6月25日 张正军教授学术报告（数学与统计学院）

This paper presents a novel nonlinear framework for the construction of flexible multivariate dependence structure(i.e., copula) from existing copulas based on a straightforward “pairwise max” rule. The newly constructed max-copula has a closed form and has strong interpretability. Compared to the classical “linear symmetric”mixture copula, the max-copula can be viewed as a “non-linear asymmetric” framework. It is capable of modeling asymmetric dependence and joint tail behavior while also offering good performance in non-extremal behavior modeling. Max-copulas that are based on single-factor and block-factor models are developed to offer parsimonious modeling for structured dependence, especially in high-dimensional applications. Combined with semi-parametric time series models, the max-copula can be used to develop flexible and accurate models for multivariate time series. A new semi-parametric composite maximum likelihood method is proposed for parameter estimation, where the consistency and asymptotic normality of estimators are established. The flexibility of the max-copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments. Real data applications in Value at Risk estimation and portfolio optimization for financial risk management demonstrate the max-copula's promising ability to accurately capture joint movements of high-dimensional multivariate stock returns under both normal and crisis regime of the financial market. This is a joint work with Zifeng Zhao.

张正军，现为美国威斯康辛大学统计系正教授、美国统计协会会士、国际数理统计协会财务总监、国际顶级期刊”商业和经济统计“副主编、”计量经济学期刊“金融工程与风险管理特刊共同主编、”泛华统计学报Statistica Sinica“副主编。

张正军教授2002年毕业于北卡罗来纳大学教堂山分校，获统计学博士学位。主要研究方向包括：金融时间序列分析、极值理论、异常气候分析、稀有疾病（癌症、帕金森综合症、奥兹海默病等等）分析、金融风险的建模和评估、市场系统性风险评估等等。

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