Title: Cubature methods to solve BSDEs: Error expansion and complexity control,
Abstract: We obtain an explicit error expansion for the solution of Backward Stochastic
Differential Equations (BSDEs) using the cubature on Wiener spaces method. The
result is proved under a mild strengthening of the assumptions needed for the
application of the cubature method. The explicit expansion can then be used to
construct implementable higher order approximations via Richardson-Romberg
extrapolation. To allow for an effective efficiency improvement of the
interpolated algorithm, we introduce an additional projection on sparse grids,
and study the resulting complexity reduction. Numerical examples are provided
to illustrate our results.