TY - JOUR
T1 - Forward-backward stochastic equations
T2 - a functional fixed point approach
AU - Nam, Kihun
AU - Xu, Yunxi
N1 - Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2023/1/2
Y1 - 2023/1/2
N2 - We introduce forward-backward stochastic equations (FBSEs) that incorporate fully-coupled forward-backward structure into backward stochastic equations (BSEs) introduced in Cheridito and Nam (Ann. Probab. 45(6A):3795–3828, 2017). Such a system generalizes the classical backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs) in previous literature. We transform an FBSE into a fixed point equation on the space of random variables and then apply general fixed point theorems to derive the existence and/or uniqueness of a solution. As a result, we obtain novel existence and/or uniqueness results for fully-coupled FBSDEs with functional drivers, which are either Lipschitz or non-Lipschitz.
AB - We introduce forward-backward stochastic equations (FBSEs) that incorporate fully-coupled forward-backward structure into backward stochastic equations (BSEs) introduced in Cheridito and Nam (Ann. Probab. 45(6A):3795–3828, 2017). Such a system generalizes the classical backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs) in previous literature. We transform an FBSE into a fixed point equation on the space of random variables and then apply general fixed point theorems to derive the existence and/or uniqueness of a solution. As a result, we obtain novel existence and/or uniqueness results for fully-coupled FBSDEs with functional drivers, which are either Lipschitz or non-Lipschitz.
KW - fixed point theorem
KW - Forward backward stochastic differential equation
KW - forward backward stochastic equation
KW - path-dependent coefficients
UR - http://www.scopus.com/inward/record.url?scp=85117603869&partnerID=8YFLogxK
U2 - 10.1080/07362994.2021.1988857
DO - 10.1080/07362994.2021.1988857
M3 - Article
AN - SCOPUS:85117603869
SN - 0736-2994
VL - 41
SP - 16
EP - 44
JO - Stochastic Analysis and Applications
JF - Stochastic Analysis and Applications
IS - 1
ER -