Southwest Jiaotong University School of Mathematics


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Robust representations of risk measures on Orlicz spaces

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Robust representations of risk measures on Orlicz spaces

Niushan Gao

Department of Mathematics

Ryerson University


In this talk, we will review the theoretical framework for quantifying market risk of financial institutions in terms of coherent risk measures, which was laid in a seminal paper of Artzner et al.~(1999). For a coherent risk measure on L^\infty, Delbaen (2002) proved that $\rho$ can be represented as the worst expectation over a class of probabilities whenever it has the Fatou property. Lately, it has been asked whether Delbaen's representation theorem holds on more general model spaces containing unbounded positions. We will present a comprehensive investigation on this problem. We characterize the Orlicz spaces over which the representation holds. We also show that the representation holds on general Orlicz spaces if the risk measure possess additional properties, e.g., law-invariance or surplus-invariance.




20087月本科毕业于北京师大大学,20138月博士毕业于加拿大阿尔伯塔大学。20144月至20168月在西南交通大学数学学院任讲师,20179月至今在加拿大Ryerson University数学系任助理教授。从事金融数学及应用分析方面的研究Mathematical Finance, Finance and Stochastics, Israel Journal of MathematicsProceedings of the American Mathematical Society等杂志发表研究论文十余篇。