讲座主题：Two armed bandit problem and nonlinear limit theorems
主讲人：陈增敬
讲座时间：2021.4.23（周五） 9：00-10：00
地点：B131
主讲人简介：  

       陈增敬，山东大学教授，博士生导师，国家级高层次人才，第十四届孙冶方经济科学奖获得者（《连续时间下的模糊性、风险性和资产收益》）,作为独立完成人完成的项目“资产定价理论中的非线性期望方法”荣获2015年度国家自然科学二等奖 [1]  。
现任山东大学齐鲁证劵金融研究院院长、山东大学数学学院院长。教育部教学指导委员会统计学分委会委员；全国概率统计学会理事、全国应用统计学会常务理事，加拿大University of Western Ontario 统计与精算科学系兼职教授。全国政协委员。

讲座摘要：

In this paper we introduce and study a Bernoulli-like model in the context of nonlinear probabilities, which we call the binary uncertainty model. This work is motivated mainly from the “two-armed bandit” problem. Our model provides a new way to study the “two-armed bandit” problem and, more generally, the distribution uncertainties. In one main result we obtain the central limit theorem for this model, and give an explicit formula for the limit distribution. The limit is shown to depend heavily on the structure of the events or the integrating functions, which demonstrate the key signature of nonlinear structure. We also establish the large deviation principle and, as an application, derive the weak law of large numbers. The large deviation rate function is identified explicitly. These limit theorems provide the theoretical foundation for statistical inferences.