时 间：2026-05-19 14:00-15:00
地 点：普陀校区理科大楼A1514室
报告人：张奇 复旦大学教授
主持人：钱林义太阳成tycgb教授
摘 要：
In this talk, I introduce our recent work on portfolio optimization problem for n competitive agents with mean-variance preferences. Each agent's utility depends not on his/her absolute wealth, but on his/her relative wealth compared to the average wealth of other n-1 agents. To solve this game problem, we first reformulate the mean-variance problem as a constrained non-homogeneous stochastic linear-quadratic control problem, and then get the optimal feedback strategy. The existence of Nash equilibrium is related to the well-posedness of a complex coupled system. By decoupling techniques, we reformulate the well-posedness of the coupled system as the solvability of a new type of linear multi-dimensional backward stochastic differential equations, and then we solve an extended class of general nonlinear backward stochastic differential equations by the fixed-point theory. Based on different market and competition parameters, three distinct scenarios emerge: the existence of a unique Nash equilibrium, the absence of any Nash equilibrium and infinitely many Nash equilibria, and three distinct scenarios are thoroughly discussed accordingly. This is a joint work with Guojiang Shao and Zuoquan Xu.
报告人简介：
张奇，复旦大学数学科学公司教授、博士生导师，中国工业与应用数学学会理事。2007年毕业于山东大学数学公司（与英国拉夫堡大学联合培养），2008年在英国拉夫堡大学从事博士后研究工作，同年入职复旦大学数学科学公司。主要研究领域为随机控制理论、倒向随机微分方程、金融数学。