A Neural RDE-based model for solving path-dependent PDEs
Bowen Fang Hao Ni Yue Wu
The concept of the path-dependent partial differential equation (PPDE) was
first introduced in the context of path-dependent derivatives in financial
markets. Its semilinear form was later identified as a non-Markovian backward
stochastic differential equation (BSDE). Compared to the classical PDE, the
solution of a PPDE involves an infinite-dimensional spatial variable, making it
challenging to approximate, if not impossible. In this paper, we propose a
neural rough differential equation (NRDE)-based model to learn PPDEs, which
effectively encodes the path information through the log-signature feature
while capturing the fundamental dynamics. The proposed continuous-time model
for the PPDE solution offers the benefits of efficient memory usage and the
ability to scale with dimensionality. Several numerical experiments, provided
to validate the performance of the proposed model in comparison to the strong
baseline in the literature, are used to demonstrate its effectiveness.