Forward-backward stochastic differential equations with monotone functionals and mean field games with common noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Ahuja, Saran¹  Ren, Weiluo¹  Yang, Tzu-Wei² 

[1] Stanford Univ, Bldg 380, Stanford, CA 94305 USA

[2] Univ Minnesota, Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA

关键词: Forward-backward stochastic differential equations;    Monotone functional;    Mean field FBSDE with conditional law;    Mean field games with common noise;   

DOI  :  10.1016/j.spa.2018.11.005

来源: Elsevier

【 摘 要 】

We consider a system of forward-backward stochastic differential equations (FBSDEs) with monotone functionals. We show that such a system is well-posed by the method of continuation similarly to Peng and Wu (1999) for classical FBSDEs. As applications, we prove the well-posedness result for a mean field FBSDE with conditional law and show the existence of a decoupling function. Lastly, we show that mean field games with common noise are uniquely solvable under a linear-convex setting and weak-monotone cost functions and prove that the optimal control is in a feedback form depending only on the current state and conditional law. (C) 2018 Published by Elsevier B.V.

【 授权许可】

Free