Cubature methods to solve BSDEs: Error expansion and complexity control

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 th...

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Bibliographic Details
Published in:arXiv.org 2019-02
Main Authors: Chassagneux, Jean-François, Garcia Trillos, Camilo A
Format: Article
Language:English
Subjects:
Algorithms
Complexity
Differential equations
Interpolation
Solution strengthening
Online Access:Get full text
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Summary: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.
ISSN:2331-8422