Deep Signature Algorithm for Path-Dependent American option pricing

In this work, we study the deep signature algorithms for path-dependent FBSDEs with reflections. We follow the backward scheme in [Hur\'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections, and combine it with the signature layer to solve American type option pricing problems while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm and provide numerical example for Amerasian option under the Black-Scholes model.