Path regularity of coupled McKean-Vlasov FBSDEs

Christoph Reisinger; Wolfgang Stockinger; Yufei Zhang

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arXiv · 2011.06664

Path regularity of coupled McKean-Vlasov FBSDEs

Christoph Reisinger·Wolfgang Stockinger·Yufei Zhang

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Abstract

This paper establishes H\"{o}lder time regularity of solutions to coupled McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). This is not only of fundamental mathematical interest, but also essential for their numerical approximations. We show that a solution triple to a MV-FBSDE with Lipschitz coefficients is 1/2-H\"{o}lder continuous in time in the $L^p$-norm provided that it admits a Lipschitz decoupling field. Special examples include decoupled MV-FBSDEs, coupled MV-FBSDEs with a small time horizon and coupled stochastic Pontryagin systems arsing from mean field control problems.

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Christoph Reisinger, Wolfgang Stockinger, Yufei Zhang. 2020-11-12. Path regularity of coupled McKean-Vlasov FBSDEs. https://arxiv.org/abs/2011.06664

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