Approximation of BSDEs with super-linearly growing generators by Euler’s polygonal line method: A simple proof of the existence

This paper develops the Euler’s polygonal line method for the backward stochastic differential equations (BSDEs) with super-linearly growing generators. The generators are allowed to be super-linearly growing in the first unknown variable y and sub-quadratic growing in the second unknown variable z when the monotonicity condition is satisfied. The convergence rate of the Euler approximation is derived, which also provides a simple proof for the existence of the solution to the monotone BSDEs. The proof is very simple and short, without involving the conventional techniques of truncating and smoothing on the generators.