报告题目：Large ranking games with diffusion control

报 告 人：周超 副教授 新加坡国立大学

邀请人：李童庆、薄立军

报告时间：2022年11月23日（周三）10：30-11：30

腾讯会议ID：533-310-789，密码：123456

报告人简介：周超，新加坡国立大学数学系副教授，量化金融研究中心主任。博士毕业于法国巴黎九大和巴黎综合理工大学，主要研究领域为：金融数学、随机控制。曾在The Annals of Applied Probability, The Annals of Probability, Mathematical Finance, Mathematics of Operations Research等多个国际权威的概率、金融数学杂志上发表文章。

报告摘要：We consider a symmetric stochastic differential game where each player can control the diffusion intensity of an individual dynamic state process, and the players whose states at a deterministic finite time horizon are among the best of all states receive a fixed prize. Within the mean field limit version of the game we compute an explicit equilibrium, a threshold strategy that consists in choosing the maximal fluctuation intensity when the state is below a given threshold, and the minimal intensity otherwise. We show that for large n the symmetric n-tuple of the threshold strategy provides an approximate Nash equilibrium of the n-player game. We also derive the rate at which the approximate equilibrium reward and the best response reward converge to each other, as the number of players n tends to infinity. Finally, we compare the approximate equilibrium for large games with the equilibrium of the two-player case. This talk is based on the joint work with Stefan Ankirchner, Nabil Kazi-Tani and Julian Wendt.