一、题目

Multivariate copula-dependent distortion risk measures

二、主讲人

胡亦钧

三、摘要

In this talk,we will introduce two new classes of multivariate risk measures, which are referred to as multivariate copula-dependent distortion risk measures. Wedefine and axiomaticallycharacterize the class of multivariate scalarcopula-dependent distortion risk measures through the tool of multivariate Choquet integral.As aby-product, this characterization can also be regarded as a multivariate extension of the univariate Greco's Representation Theorem. Furthermore, based on the representations for the multivariate scalar copula-dependent distortion risk measures, wewillintroduce the class of multivariate vector-valued copula-dependent distortion risk measures, and their properties of copula-dependent monotonicity, translation invariance, positive homogeneity and pi-comonotone additivity are shown. Finally, we present several examples,among which one example introduces a new class of vector-valued risk measures, while the others demonstrate the comparisons of the introduced multivariate vector-valued distortion risk measures with those vector-valued risk measures known as in the literature.

This talk is based on a joint work with Suo Gong and Linxiao Wei.

四、主讲人介绍

胡亦钧，武汉大学数学与统计学院，教授,博士生导师。1993年毕业于武汉大学数学系、获博士学位并留校任教。主要从事金融风险度量、保险数学、概率极限理论等相关领域的研究。先后主持完成国家自然科学基金面上项目多项，在保险、金融、概率统计等领域的国内外专业刊物上发表论文60余篇。曾先后应邀访问美国Maryland大学、加拿大York大学、芬兰Helsinki大学、香港大学、香港科技大学、香港浸会大学。曾获湖北省自然科学奖二等奖（2003年），教育部高校优秀骨干教师（2003年），教育部“新世纪优秀人才支持计划”（2004年）的奖励和荣誉称号。

五、邀请人

吴盼玉

六、时间

11月15日（周一）15:00-16:00

七、地点

腾讯会议ID: 271 744 043

八、主办方

山东大学数学学院