  As is known, an option price is a solution to a certain partial differential
equation (PDE) with terminal conditions (payoff functions). There is a close
association between the solution of PDE and the solution of a backward
stochastic differential equation (BSDE). We can either solve the PDE to obtain
option prices or solve its associated BSDE. Recently a deep learning technique
has been applied to solve option prices using the BSDE approach. In this
approach, deep learning is used to learn some deterministic functions, which
are used in solving the BSDE with terminal conditions. In this paper, we extend
the deep-learning technique to solve a PDE with both terminal and boundary
conditions. In particular, we will employ the technique to solve barrier
options using Brownian motion bridges.
