MEAN-FIELD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND NONLOCAL PDES WITH QUADRATIC GROWTH

• 成果类型: Article
• 署名作者: Hao, Tao; Hu, Ying; Tang, Shanjian; Wen, Jiaqiang
• 署名单位: Shandong University of Finance & Economics; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Fudan University; Fudan University; Southern University of Science & Technology; Southern University of Science & Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2167
• 发表日期: 2025
• 页码: 2128-2174
• 关键词: viscosity solutions; Generators; BSDEs; sdes

摘要

In this paper, we study 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,PY, PZ) 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.