报 告 人：嵇少林 山东大学
报告时间：2020年12月22日 14:30-17:00
地 点：腾讯会议 （ID： 610 835 717）
摘 要：In this talk, we study the Neyman-Pearson theory for convex expectations (convex risk measures) on $L^{\infty}(\mu)$. Without assuming that the level sets of penalty functions are weakly compact, a new approach is proposed to find a representative pair $(Q^{\ast}, P^{\ast})$ such that the optimal tests are just the classical Neyman-Pearson tests between the representative probabilities $Q^{\ast}$ and $P^{\ast}$. The key observation is that the feasible test set is compact in the weak$^{\ast}$ topology by a generalized result of Banach-Alaoglu theorem. Then the minimax theorem can be applied and the representative probability $Q^{\ast}$ is found first. Secondly, under the probability $Q^{\ast} $, we find the representative probability measure $P^{\ast}$ by solving a dual problem. Finally, we apply our results to a shortfall risk minimizing problem in an incomplete financial market.
报告人简介
嵇少林，山东大学教授，博士生导师，是彭实戈院士创新学术团队成员之一，2011年入选教育部新世纪优秀人才支持计划。研究领域：金融数学、随机控制和非线性期望理论。近年来，嵇少林教授在Review of Financial Studies, Probability Theory and Related Fields和SIAM Control and Optimization等杂志上发表了一系列的成果。研究的问题包括模型不确定下的资产定价公式、非线性期望下Neyman - Pearson基本引理和G-布朗运动驱动下的倒向随机微分方程理论。
