西南交通大学数学学院邀请高牛山老师作了一场题为“Unbounded order convergence and w*-representations of risk measures(无界阶收敛以及w * -风险的措施表示)”的讲座,数学学院现有铁道部和四川省重点学科一个:应用数学;硕士学位点三个:基础数学、应用数学、概率论与数理统计;本科专业三个:数学与应用数学、信息与计算科学、统计学。讲座的主要内容是:
在这次演讲中,我们将讨论无限阶收敛的概念和它的一些应用,以功能分析和金融数学。具体而言,我们将讨论三个议题:(1)无界阶收敛的功能分析方面;(2)申请顺序连续preduals的研究;(3)应用的风险的措施表示理论。特别是,我们会告诉每一个Banach格至多有一个阶连续前双和表征那些确实有这样一个predual。我们也将展示双Orlicz空间,这使我们能够建立W *的一些秩序拓扑性质 - 的风险的措施表示。讲座是基于弗拉基米尔Troitsky和Foivos Xanthos联合工作。
原文:In this talk, we will discuss the notion of unbounded order convergence and some of its applications to Functional Analysis and Mathematical Finance. Specifically, we will cover three topics: (1) functional analytic aspects of unbounded order convergence; (2) application to the study of order continuous preduals; (3)application to representation theory of risk measures. In particular, we will show that every Banach lattice has at most one order continuous pre-dual and characterize those which do have such a predual. We will also demonstrate some order-topology properties of dual Orlicz spaces, which enable us to establish w*-representations of risk measures. The talk is based on joint work with Vladimir Troitsky and Foivos Xanthos.