一、主讲人

Roxana Dumitrescu，法国巴黎综合理工学院教授

二、讲座时间

2026年5月22日（星期五）19:30-20:30

三、主办单位

山东大学数学交叉科学研究中心

《概率、不确定性与定量风险（英文）》编辑部

四、主讲人简介

Roxana Dumitrescu is Professor of Financial Mathematics at ENSAE-CREST, Institut Polytechnique de Paris, since 2024. She is also Co-Director of the Research Master Statistics, Finance and Insurance of Institut Polytechnique de Paris and Scientific Co-director of the Energy 4Climate Center. Formerly, she was Associate Professor and Director of the MSc in Financial Mathematics at King's College London from 2016 to 2024. She received a PhD in Applied Mathematics from the University Paris-Dauphine in 2015, under the supervision of Professor Bruno Bouchard. Since January 2024, she has been serving as Associate Editor of the journalMathematics and Financial Economics. Her research interests encompass Financial Mathematics, Stochastic Control, Stochastic Differential Games, Mean-Field Games, Backward Stochastic Differential Equations, Energy Markets, and Machine Learning. She has been awarded the 2026 EIF–SCOR Foundation Prize of the Institut Louis Bachelier in the category of Best Young Researcher in Finance and Insurance.

五、报告摘要

We propose a novel probabilistic formulation for mean field games of optimal stopping (MFG-OSs) in the presence of randomized strategies. We characterize the mean field equilibrium through a new class of BSDEs, termed McKean-Vlasov reflected backward stochastic differential equations (MKV-RBSDEs). An equilibrium is characterized by a quintuple (X,Y,Z,A,L), whereLis an adapted, [0,1]-valued, non-increasing càdlàg process, representing a randomized stopping strategy. The optimality of the randomized stopping strategy is endogenized directly via two novel Skorokhod-type conditions. We establish the existence of equilibria by applying the Kakutani–Fan–Glicksberg fixed-point theorem to a set-valued best-response map. Under alternative monotonicity assumptions, we derive an existence result using Tarski's fixed-point theorem, and we provide a constructive proof of existence of maximal and minimal equilibria. Furthermore, we prove the uniqueness of the equilibrium under specific conditions. We also show that a mean field equilibrium induces an approximate Nash equilibrium for the associatedN-player stopping game. Finally, we connect our probabilistic formulation to the analytical approach, which is characterized by a system of constrained partial differential equations (joint work with Andrea Cosso and Laura D'Andolfi).

六、参会方式

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