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Mathematics of Computation

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Cubature method to solve BSDEs: Error expansion and complexity control


Authors: Jean-Francois Chassagneux and Camilo A. Garcia Trillos
Journal: Math. Comp. 89 (2020), 1895-1932
MSC (2010): Primary 60H35, 65C30
DOI: https://doi.org/10.1090/mcom/3522
Published electronically: March 10, 2020
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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.


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Additional Information

Jean-Francois Chassagneux
Affiliation: Laboratoire de Probabilités, Statistique et Modélisation, Université Paris Diderot, 5 Rue Thomas Mann, 75013 Paris, France
Email: chassagneux@math.univ-paris-diderot.fr

Camilo A. Garcia Trillos
Affiliation: Department of Mathematics, University College London, Gower Street, Bloomsbury, London WC1E 6BT, United Kingdom
Email: camilo.garcia@ucl.ac.uk

DOI: https://doi.org/10.1090/mcom/3522
Received by editor(s): February 3, 2017
Received by editor(s) in revised form: January 18, 2019
Published electronically: March 10, 2020
Additional Notes: The second author’s research was supported in part by OpenGamma Ltd.
Article copyright: © Copyright 2020 American Mathematical Society