华东师范大学经济与管理学部邀请Yaozhong Hu教授作了一场题为“Singular mean-filed control games with applications to optimal harvesting and investment problems(奇异平均场控制场比赛与应用最优收获和投资问题)”的讲座。华东师范大学有中国哲学、职业技术教育学、汉语言文字学、中国古代文学、中国近现代史、世界史、基础数学、光学、物理化学、人文地理学、微电子学与固体电子学、计算机软件与理论等上海市重点学科。讲座的主要内容是:
我们研究奇异平均场控制问题和奇异平均场两名选手随机微分游戏。得到的最优控制和纳什均衡双方的充分必要条件。根据一些假设为单数平均场控制的最优性条件被减少到一个反射椭圆问题,其解决方案被证明唯一地存在。应用程序是给随机平均场系统,一定的不确定性下的最优投资不可逆转的最优收获和平均场奇异的投资游戏。
原文:We study singular mean field control problems and singular mean field two players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Applications are given to optimal harvesting of stochastic mean-field systems, optimal irreversible investments under certain uncertainty and to mean-field singular investment games.