On path-dependent multidimensional forward-backward SDEs
Hu, Kaitong; Ren, Zhenjie; Touzi, Nizar (2022), On path-dependent multidimensional forward-backward SDEs, Numerical Algebra, Control and Optimization (NACO). 10.3934/naco.2022010
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Article accepté pour publication ou publiéDate
2022Journal name
Numerical Algebra, Control and Optimization (NACO)Publication identifier
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Hu, KaitongCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Touzi, Nizar
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Abstract (EN)
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 coefficients of the forward-backward SDE at time can depend on the whole path of the forward process up to time . 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 decoupling 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.Subjects / Keywords
Forward-Backward SDE; Backward Stochastic Riccati Equations; decoupling random field; Characteristic BSDERelated items
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