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Cubature methods to solve BSDEs: Error expansion and complexity control

Chassagneux, J-F; Trillos, CAG; (2020) Cubature methods to solve BSDEs: Error expansion and complexity control. Mathematics of Computation , 89 (324) pp. 1895-1932. 10.1090/mcom/3522. Green open access

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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.

Type: Article
Title: Cubature methods to solve BSDEs: Error expansion and complexity control
Open access status: An open access version is available from UCL Discovery
DOI: 10.1090/mcom/3522
Publisher version: https://doi.org/10.1090/mcom/3522
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10089028
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