报 告 人： 韩霞 南开大学数学科学学院 讲师

报告时间： 9月11日（星期三晚上6:30-7:30）

报告地点：#腾讯会议：362-683-9628

报告摘要：Mean-deviation models, along with the existing theory of coherent risk measures,  are well studied in the literature. We characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a risk-weighting function to the deviation part. The  form is a combination of the deviation-related functional and the expectation, and such measures  belong to the class of consistent risk measures.  The monotonic mean-deviation measures admit an axiomatic foundation via preference relations. By further assuming the convexity and linearity of the risk-weighting function, the characterizations for convex and coherent risk measures are obtained, giving rise to many new explicit examples of convex and nonconvex consistent risk measures. Further, we specialize in the convex case of the monotonic mean-deviation measure and obtain its dual representation. The asymptotic consistency and normality of the natural estimators of the monotonic mean-deviation measures are established. Finally, some applications of monotonic mean-deviation measures are discussed.

报告人简介：韩霞，南开大学数学科学学院概率统计系讲师，2020年7月获得南京师范大学统计学博士学位；2020年9月至2022年8月在加拿大滑铁卢大学精算与统计系从事两年博士后工作。主要研究方向为随机最优控制在金融保险市场中的应用、风险度量。在《Scandinavian Actuarial Journal》、《Insurance: Mathematics and Economics, 》、《SIAM Journal on Control and Optimization》、《Mathematical Finance》等期刊发表学术论文。