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

Saran Ahuja, Weiluo Ren and Tzu-Wei Yang

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3859-3892

Abstract: 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.

Keywords: Forward–backward stochastic differential equations; Monotone functional; Mean field FBSDE with conditional law; Mean field games with common noise (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2018.11.005

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