  Backward stochastic differential equations (BSDEs) belong nowadays to the
most frequently studied equations in stochastic analysis and computational
stochastics. BSDEs in applications are often nonlinear and high-dimensional. In
nearly all cases such nonlinear high-dimensional BSDEs cannot be solved
explicitly and it has been and still is a very active topic of research to
design and analyze numerical approximation methods to approximatively solve
nonlinear high-dimensional BSDEs. Although there are a large number of research
articles in the scientific literature which analyze numerical approximation
methods for nonlinear BSDEs, until today there has been no numerical
approximation method in the scientific literature which has been proven to
overcome the curse of dimensionality in the numerical approximation of
nonlinear BSDEs in the sense that the number of computational operations of the
numerical approximation method to approximatively compute one sample path of
the BSDE solution grows at most polynomially in both the reciprocal $1/
\varepsilon$ of the prescribed approximation accuracy $\varepsilon \in
(0,\infty)$ and the dimension $d\in \mathbb N=\{1,2,3,\ldots\}$ of the BSDE. It
is the key contribution of this article to overcome this obstacle by
introducing a new Monte Carlo-type numerical approximation method for
high-dimensional BSDEs and by proving that this Monte Carlo-type numerical
approximation method does indeed overcome the curse of dimensionality in the
approximative computation of solution paths of BSDEs.
