Mean-Field Doubly Reflected Forward-Backward SDEs with Optional Barriers and $L^p$-Data

Erhan Bayraktar; Maurycy Rzymowski

Mean-Field Doubly Reflected Forward-Backward SDEs with Optional Barriers and $L^p$-Data

Probability 2026-08-05 v1

Authors: Erhan Bayraktar , Maurycy Rzymowski

Abstract

We study mean-field doubly reflected forward-backward stochastic differential equations with two optional barriers satisfying a strong Mokobodzki condition. For $L^p$ -data, $p\in(1,2]$ , we prove existence and uniqueness on sufficiently short time horizons when the coefficients may depend on the joint law of $(X,Y,Z)$ . Under an additional monotonicity condition and using an exponentially weighted norm, we also obtain a global-in-time result for $p=2$ . The setting is motivated by recursive mean-field Dynkin games and game-option valuation with irregular payoff barriers.

Keywords

mean-field FBSDEs doubly reflected optional barriers mokobodzki condition dynkin games game options

Cite

@article{arxiv.2608.04937,
  title  = {Mean-Field Doubly Reflected Forward-Backward SDEs with Optional Barriers and $L^p$-Data},
  author = {Erhan Bayraktar and Maurycy Rzymowski},
  journal= {arXiv preprint arXiv:2608.04937},
  year   = {2026}
}