  We propose a deep signature/log-signature FBSDE algorithm to solve
forward-backward stochastic differential equations (FBSDEs) with state and path
dependent features. By incorporating the deep signature/log-signature
transformation into the recurrent neural network (RNN) model, our algorithm
shortens the training time, improves the accuracy, and extends the time horizon
comparing to methods in the existing literature. Moreover, our algorithms can
be applied to a wide range of applications such as state and path dependent
option pricing involving high-frequency data, model ambiguity, and stochastic
games, which are linked to parabolic partial differential equations (PDEs), and
path-dependent PDEs (PPDEs). Lastly, we also derive the convergence analysis of
the deep signature/log-signature FBSDE algorithm.
