華東師范大學(xué)經(jīng)濟(jì)與管理學(xué)部邀請Yaozhong Hu教授作了一場題為“Singular mean-filed control games with applications to optimal harvesting and investment problems(奇異平均場控制場比賽與應(yīng)用最優(yōu)收獲和投資問題)”的講座。華東師范大學(xué)有中國哲學(xué)、職業(yè)技術(shù)教育學(xué)、漢語言文字學(xué)、中國古代文學(xué)、中國近現(xiàn)代史、世界史、基礎(chǔ)數(shù)學(xué)、光學(xué)、物理化學(xué)、人文地理學(xué)、微電子學(xué)與固體電子學(xué)、計(jì)算機(jī)軟件與理論等上海市重點(diǎn)學(xué)科。講座的主要內(nèi)容是：

　　我們研究奇異平均場控制問題和奇異平均場兩名選手隨機(jī)微分游戲。得到的最優(yōu)控制和納什均衡雙方的充分必要條件。根據(jù)一些假設(shè)為單數(shù)平均場控制的最優(yōu)性條件被減少到一個(gè)反射橢圓問題，其解決方案被證明唯一地存在。應(yīng)用程序是給隨機(jī)平均場系統(tǒng)，一定的不確定性下的最優(yōu)投資不可逆轉(zhuǎn)的最優(yōu)收獲和平均場奇異的投資游戲。

　　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.