Kaitong Hu, Zhenjie Ren, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-dependent we mean that the coeffcients of the forward-backward SDE at time t can depend on the whole path of the forward process up to time t. Such a situation appears when solving path-dependent stochastic control problems by means of variational calculus. At the heart of our analysis is the construction of a decoupling random field on the path space. We first prove the existence and the uniqueness of de-coupling field on small time interval. Then by introducing the characteristic BSDE, we show that a global decoupling field can be constructed by patching local solutions together as long as the solution of the characteristic BSDE remains bounded. Finally, we provide a stability result for path-dependent forward-backward SDEs.

Original languageEnglish (US)
JournalNumerical Algebra, Control and Optimization
StatePublished - 2022


  • Backward Stochastic Riccati Equations
  • Characteristic BSDE
  • De-coupling random field
  • Forward-Backward SDE

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Control and Optimization
  • Applied Mathematics


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