Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing

We report two methods for solving FBSDEs of path-dependent types in high-dimensions. Inspired by the work from [31], [32], and [20], we propose deep learning frameworks for solving such problems using path signatures as underlying features. Our two methods (forward/backward) demonstrate comparable/better accuracy and efficiency compared to the state of the art [14], [13], and [18]. More importantly, leveraging the techniques developed in [5], we are able to solve the problem of high dimension (100 and above), which is a limitation in [14] and [13]. We also provide convergence proofs for both methods with the proof of the the forward method following similar lines to [14], and the backward methods inspired by [16] in the Markovian case.