Deep Signature FBSDE Algorithm
This incremental improvement addresses FBSDEs for applications like option pricing and stochastic games, which are linked to PDEs and path-dependent PDEs.
The authors tackled solving forward-backward stochastic differential equations (FBSDEs) with state and path dependent features by proposing a deep signature/log-signature FBSDE algorithm, which reduces training time, improves accuracy, and extends the time horizon compared to existing methods.
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.