学术报告

题      目：Random distortion risk measures

报  告  人：臧鑫  副教授  (邀请人：杨舟 )

                                    北京交通大学数学与统计学院

时      间：12月22日  16：00-17：00

地     点：数科院西楼二楼会议室

报告人简介:

        臧鑫，北京交通大学数学与统计学院数据科学系，博士毕业于北京大学数学科学学院金融数学系。研究方向为量化风险管理和应用概率论，研究成果发表于Quantitative Finance, Probability in the Engineering and Informational Sciences等杂志。

摘      要：

        This paper presents one type of random risk measures, named as the random distortion risk measure. The random distortion risk measure is a generalization of the traditional deterministic distortion risk measure by randomizing the deterministic distortion function and the risk distribution respectively, where a stochastic distortion is introduced to randomize the distortion function, and a sub-sigma-algebra is introduced for illustrating the influence of the known information on the risk distribution. Some theoretical properties of the random distortion risk measure are provided, such as normalization, conditional positive homogeneity, conditional comonotonic additivity, monotonicity in stochastic dominance order, and continuity from below, and a method for specifying the stochastic distortion and the sub-sigma-algebra is provided. Based on some stochastic axioms, the representation theorem of the random distortion risk measure is proved. For considering the randomization of a given deterministic distortion risk measure, some families of random distortion risk measures are introduced with the stochastic distortions constructed from a Poisson process, a Brownian motion and a Dirichlet process respectively. And a numerical analysis is carried out for showing the influence of the stochastic distortion and the sub-sigma-algebra by focusing on the sample mean, variance, skewness, kurtosis, and the tail behavior of the random distortion risk measures.

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