TY - JOUR
T1 - ON PATH-DEPENDENT MULTIDIMENSIONAL FORWARD-BACKWARD SDES
AU - Hu, Kaitong
AU - Ren, Zhenjie
AU - Touzi, Nizar
N1 - Publisher Copyright:
© 2022, American Institute of Mathematical Sciences. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Backward Stochastic Riccati Equations
KW - Characteristic BSDE
KW - De-coupling random field
KW - Forward-Backward SDE
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U2 - 10.3934/naco.2022010
DO - 10.3934/naco.2022010
M3 - Article
AN - SCOPUS:85133669188
SN - 2155-3289
VL - 2022
JO - Numerical Algebra, Control and Optimization
JF - Numerical Algebra, Control and Optimization
ER -