Title: Path-dependent fractional smoothness of forward-backward stochastic differential equations
Abstract:
The decoupling method introduced in Geiss & Ylinen in 2021 shows the relation between the smoothness properties of backward stochastic differential equations(BSDE) and the decoupling variation of the solution.
We investigate the forward-backward stochastic differential equation.
Xt =η + ∫t0 b(s,Xs,Ys,Zs) d s + ∫t0 σ(s,Xs,Ys) d Ws
Yt = g(XT) +∫Tt f(s,Xs,Ys,Zs) d s - ∫Tt Z_s d Ws,
with the Lipschitz constant of the function b and σ with respect to the Y and Z process relying on time. We proved the global existence for the FBSDE under the certain condition, and applied the decoupling method to get the path-dependent Besov smoothness of real interpolation of the solution.
