Cubature methods to solve BSDEs: Error expansion and complexity control
Probability
2019-02-22 v2
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 finite grids through interpolation operators. We study the resulting complexity reduction in the case of the linear interpolation.
Cite
@article{arxiv.1702.00999,
title = {Cubature methods to solve BSDEs: Error expansion and complexity control},
author = {Jean-François Chassagneux and Camilo A. Garcia Trillos},
journal= {arXiv preprint arXiv:1702.00999},
year = {2019}
}