报告题目： Two armed bandit problem and nonlinear limit theorems
报 告 人： 陈增敬 教授 山东大学
报告时间： 2021年12月15日 15：00-16：00
报告地点： 腾讯会议：512-562-169
会议链接： https://meeting.tencent.com/dm/xN7y9v07hZmS
校内联系人：韩月才 hanyc@jlu.edu.cn
报告摘要：In this talk, we will introduce 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.
报告人简介：陈增敬，山东大学必威经理，教授。主要研究方向包括金融数学、倒向随机微分方程、计量经济学等，科研成果发表在Annals of Probability 和 Econometrica等国际期刊上。其中，与美国艺术与科学院士、著名经济学家Epstein合作发表在国际顶级经济刊Econometrica上的论文是大陆学者第一篇发表在该顶级期刊的论文，得到了被称为Chen-Epstein的资产定价公式，被诺贝尔经济奖获得者Sargent和Hansen等国际著名专家引用或推广。陈增敬教授是教育部第六批“长江学者”奖励计划特聘教授，国家杰出青年科学基金获得者和第十四届孙冶方经济科学奖获得者。作为独立完成人获2015年度国家自然科学二等奖。
