Forward-Backward Stochastic Differential Equations and their Applications

By J. Ma, J. Yong. 2007

788 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/d39d6e3fce081e1e792803951f16aa0d29d27bb5

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Citations in the corpus

Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, methodology): “In order to obtain an explicit representation of the optimal control, we use a decoupling technique inspired by the four-step scheme introduced in [25,26] for general FBSDEs to solve the optimality system.”
Probabilistic Analysis of Mean-Field Games (2012, methodology): “ts are based on probabilistic a priori estimates obtained from tailor-made versions of the stochastic maximum principle which we derive in Section 2. The reader is referred to the book of Ma and Yong [22] for background material on adjoint equations, FBSDEs and the stochastic maximum principle appro”
Option pricing with an illiquid underlying asset market (2005, methodology): “…we use the idea of a four-step scheme for forward and backward stochastic differential equations (FBSDEs) (see Ma, Protter, and Yong (1994), Yong (1999), Yong and Zhou (1999)) to derive a generalized, nonlinear BlackScholes partial differential equation (PDE) for computing the replicating…”
Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method (2006, methodology): “Let us recall that under (A1)–(A2), for any h(·) ∈ L(2)F (0, T ; lR) and η ∈ L2FT (Ω; lR), the following linear backward stochastic differential equation (BSDE, for short) admits a unique adapted solution (Y (·), Z(·)) ([22], [19]): dY (t) = −[A>(t)Y (t) + C>(t)Z(t) + h(t)]dt + Z(t)dW (t), Y (T ) = ”
Time discretization and Markovian iteration for coupled FBSDEs (2008, background): “In particular, if by = σy = 0, then the forward equation in (1.1) does not depend on the backward one and, thus, (1.1) is decoupled.”
A Probabilistic Approach to Mean Field Games with Major and Minor Players (2014, background): “The concept of (deterministic) decoupling field lies at the core of many investigations of the well-posedness of standard FBSDEs, see for example [14, 22].”
Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model (2009, background): “The FBSDEs theory is presented in the monograph [15].”
Error expansion for the discretization of backward stochastic differential equations (2006, methodology): “(2) We assume standard Lipschitz properties on the coefficients, which ensure existence and uniqueness in appropriate L2-spaces (see Pardoux and Peng [18], or Ma and Yong [14] for numerous references).”
Linear−quadratic optimal control and nonzero‐sum differential game of forward−backward stochastic system (2012, methodology): “For more details of coupled FBSDE theory, we refer to the book by Ma and Yong [22] and the references therein.”
Weak existence and uniqueness for forward–backward SDEs (2006, methodology): “For this reason, we do not discuss in detail the application fields of the FBSDE theory and just refer to the monograph of Ma and Yong [29] for typical examples arising in mathematical finance or in control problems.”
Continuous-time dynamic risk measures by backward stochastic Volterra integral equations (2007, background): “See [2,4,8,9], and references cited therein for systematic discussions on BSDEs.”
Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations --- Time-Consistent Solutions (2013, positive): “Inspired by [18], we suppose Y (s, t) = P (s, t)X∗(s) + P̄ (s, t)Et[X ∗(s)], s ∈ [t, T ], for some deterministic functions P (· , ·) and P̄ (· , ·).”
A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations (2011, methodology): “3), we use the idea of decoupling inspired by the Four-Step Scheme ([21, 22]).”
General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions (2012, background): “As important byproducts in the study of the above finite dimensional stochastic control problems, one introduced some new mathematical tools, say, backward stochastic differential equations (BSDEs, for short) and forward-backward stochastic differential equations ([6, 7, 23] and [19, 29]), which are”
BSDE, path-dependent PDE and nonlinear Feynman-Kac formula (2011, methodology): “Since this pioneering work, the theory of BSDEs has become a useful tool to solve the problems of elliptic and parabolic PDEs (see Ma and Yong [12], Pardoux [15] and the references therein).”