报告人：杜凯 教授
报告题目：Indefinite Linear-Quadratic Mean-Field Game of Regime-Switching System
报告时间：2026年5月16日（周六）上午9：00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
杜凯，山东大学数学学院教授、泰山学者青年专家。主要研究领域为随机最优控制与平均场博弈、正倒向随机微分方程与金融数学，在IEEE\CAA JAS、JDE、CMS等期刊发表学术论文10余篇。主持国家自然科学基金面上项目等科研项目5项，入选国家博士后创新人才支持计划，获得第十六届钟家庆数学奖，参与获得2026年山东省教学成果特等奖。
报告摘要：
In this talk, we introduce an indefinite mean-field game with Markov jump parameters. One notable aspect is the relaxation of the assumption regarding the positivity or non-negativity of weight matrices within costs. By virtue of mean-field methods and decomposition techniques, we have derived decentralized strategies presented by Hamiltonian systems and a new type of consistency condition system. These systems consist of fully coupled regime-switching forward-backward stochastic differential equations that do not conform to the Monotonicity condition. The well-posedness of these strategies is established by employing a relaxed compensator method with an easily verifiable Condition (RC) and the decomposition technique. Furthermore, we demonstrate that the resulting decentralized strategies achieve an epsilon-Nash equilibrium in the indefinite case without any assumptions on admissible control sets using novel estimates of the disturbed state and cost function.