讲座主题：STRATEGIC LIMIT THEOREMS ASSOCIATED WITH BANDIT PROBLEMS
主讲人：陈增敬
讲座时间：2022年10月16日星期日 上午10:00-11:00
讲座地点：线上：腾讯会议ID: 784-824-052
主讲人简介：
陈增敬，山东大学教授，博士生导师，山东大学金融研究院院长，山东国家应用数学中心常务副主任。伯努利学会2022-2023年东亚及太平洋区域委员会主席，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。陈增敬教授是国家高层次人才、第十四届孙冶方经济科学奖获得者，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，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。
讲座摘要：
Motivated by the study of asymptotic behaviour of the bandit problems, we obtain several strategic limit theorems including the strategic law of large numbers, the strategic large deviation principle and the strategic central limit theorem. Different from the classical limit theorems. we develop sampling strategic limit theorems that generate the maximum average reward, our law of large numbers with strategy identifies all possible limits that are achievable under various strategies. The large deviation principle provides the maximum decay probabilities for deviations from the limiting domain. To describe the fluctuations around averages we obtain several central limit theorems under optimal strategies.The limits in these theorems are identified explicitly. and depend heavily on the structure of the events or the integrating functions and strategies. This demonstrates the key signature of the learning structure. It also lays the theoretical foundation for statistical raison inference in deter-mining the arm that offers the higher mean reward.
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