報告人：杜凱 教授
報告題目：Indefinite Linear-Quadratic Mean-Field Game of Regime-Switching System
報告時間：2026年5月16日（周六）上午9：00
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
杜凱，山東大學數學學院教授、泰山學者青年專家。主要研究領域為隨機最優控制與平均場博弈、正倒向隨機微分方程與金融數學，在IEEE\CAA JAS、JDE、CMS等期刊發表學術論文10余篇。主持國家自然科學基金面上項目等科研項目5項，入選國家博士后創新人才支持計劃，獲得第十六屆鐘家慶數學獎，參與獲得2026年山東省教學成果特等獎。
報告摘要：
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.