Series Academic Report of Jiangsu Provincial Center for Applied Mathematics (China University of Mining and Technology)
Title: Mean-field Backward Stochastic Differential Equations and Nonlocal PDEs with Quadratic Growth
Speaker: Professor Ying Hu, University of Rennes 1, France
Time: July 2, 2025 (Wednesday), 16:30-17:30
Venue: Room A321, School of Mathematics
Abstract:
In this talk, I will introduce general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, using some new ideas, we prove the existence and uniqueness of local and global solutions for a one-dimensional mean-field BSDE when the generator ( g(t,Y, Z, P_Y, P_Z) ) has quadratic growth in ( Z ) and the terminal value is bounded. Second, we derive a comparison theorem for general mean-field BSDEs by applying the Girsanov transform. Third, within this framework, we use the mean-field BSDE to provide a probabilistic representation of the viscosity solution for a nonlocal partial differential equation (PDE, for short) as an extended nonlinear Feynman–Kac formula, which yields the existence and uniqueness of the solution to the PDE. Finally, we prove the convergence of the particle systems to general mean-field BSDEs with quadratic growth and give the corresponding convergence rate.
About the Speaker:
Ying Hu is a Distinguished Professor at the University of Rennes 1, France, and an internationally renowned expert in stochastic analysis and stochastic control. His research interests primarily focus on stochastic processes, partial differential equations, and stochastic control, with outstanding contributions particularly in the field of backward stochastic differential equations. He has published over 100 high-level academic papers in top-tier international journals such as PTRF (Probability Theory and Related Fields), AAP (Annals of Applied Probability), SICON (SIAM Journal on Control and Optimization), JFA (Journal of Functional Analysis), MF (Mathematical Finance), FS (Finance and Stochastics), and SPA (Stochastic Processes and their Applications).
