de Raynal, PEC;
Trillos, CAG;
(2015)
A cubature based algorithm to solve decoupled McKean-Vlasov forward-backward stochastic differential equations.
Stochastic Processes and their Applications
, 125
(6)
pp. 2206-2255.
10.1016/j.spa.2014.11.018.
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Abstract
We propose a new algorithm to approximate weakly the solution of a McKean–Vlasov SDE. Based on the cubature method of Lyons and Victoir (2004), the algorithm is deterministic differing from the usual methods based on interacting particles. It can be parametrized in order to obtain a given order of convergence. Then, we construct implementable algorithms to solve decoupled Forward–Backward Stochastic Differential equations (FBSDE) of McKean–Vlasov type, which appear in some stochastic control problems in a mean field environment. We give two algorithms and show that they have convergence of order one and two under appropriate regularity conditions.
| Type: | Article |
|---|---|
| Title: | A cubature based algorithm to solve decoupled McKean-Vlasov forward-backward stochastic differential equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.spa.2014.11.018 |
| Publisher version: | http://doi.org/10.1016/j.spa.2014.11.018 |
| 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. |
| Keywords: | Cubature, McKean–Vlasov processes, BSDE, Mean field games, Non-local PDE |
| 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/1464371 |
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