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.
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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 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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