Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with jumps
Year: 2026
Type: preprint
Abstract: We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integrability assumptions on the coefficients, we show that the MLP algorithm does not suffer from the curse of dimensionality when approximating the solution of the McKean-Vlasov SDE. The latter means that its computational cost grows at most polynomially in both the state-space dimension of the SDE and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate the practical applicability of the MLP algorithm for two different McKean-Vlasov SDEs in dimensions up to 200.
Source: arXiv (Cornell University)
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: Ministry of Education, India
OpenAlex ID: W7221096527