華東師范大學(xué)經(jīng)濟(jì)與管理學(xué)部邀請(qǐng)Yaozhong Hu教授作了一場(chǎng)題為“Singular mean-filed control games with applications to optimal harvesting and investment problems(奇異平均場(chǎng)控制場(chǎng)比賽與應(yīng)用最優(yōu)收獲和投資問(wèn)題)”的講座。華東師范大學(xué)有中國(guó)哲學(xué)、職業(yè)技術(shù)教育學(xué)、漢語(yǔ)言文字學(xué)、中國(guó)古代文學(xué)、中國(guó)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(chǎng)控制問(wèn)題和奇異平均場(chǎng)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(chǎng)控制的最優(yōu)性條件被減少到一個(gè)反射橢圓問(wèn)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(chǎng)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(chǎng)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.