报告人：张霜剑教授（复旦大学）

时 间：2025年10月24日星期五上午11:00-12:00

地 点：数理楼135教室

题 目：Monopolist problem: Existence, uniqueness, regularity of the optimal solutions and more

摘 要：The monoplist problem is one of the central problems in microeconomics with many applications. Existence, uniqueness, convexity/concavity, regularity, and characterization of the solutions have been widely studied since 1970s. For multidimensional spaces of agents and products, Rochet and Choné (Econometrica, 1998) reformulated this problem to a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of Rochet-Choné to a novel free boundary problem, giving the first analytical description of an overlooked market segment, where the regularity built by Caffarelli-Lions plays a crucial role——an extension of their regularity work to the quasilinear case is also recently studied.

In this talk, I will first introduce the historical work on the principal-agent framework under the context of the monopolist problem before moving to the recent progress. The results profoundly connect with the Optimal Transport theory, a powerful tool with potential applications in many areas. This talk contains my joint work with Robert J. McCann and Cale Rankin.

报告人简介：张霜剑，复旦大学数学科学学院青年研究员，博士生导师。2023年入选国家高层次青年人才。2012年本科毕业于南开大学陈省身班；2018年博士毕业于多伦多大学数学系；博士毕业后曾在巴黎高科国立统计与经济管理学院、巴黎高等师范学院、滑铁卢大学从事博士后研究。2023年9月至今任职于复旦大学数学科学学院，主要研究为最优输运理论在经济金融中的应用，其研究成果发表在Communications on Pure and Applied Mathematics、Economic Theory、Journal of Mathematical Economics、Conference on Learning Theory等。