勷勤数学•专家报告

题      目：Monopolist's profit-maximization v.s. screening problems: a PDE point of view

报  告  人：张霜剑  教授  (邀请人：杨舟)

                                    武汉大学

时      间：11月23日  09：00-10：00

地     点：数科院西楼二楼会议室

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、Mathematical Models and Methods in Applied Sciences、Economic Theory、Journal of Mathematical Economics、Conference on Learning Theory等。

摘      要：

       The principal-agent 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 after Mirrlees and Spence in the 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. 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.

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