Work

First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems

Year: 2021

Type: article

Abstract: In this paper, we derive fully implementable first-order time-stepping schemes for McKean-Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean-Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order moments. In addition, numerical examples are presented which support our theoretical findings.

Source: Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

DOI: 10.1098/rspa.2020.0258

Authors: Jianhai Bao, Christoph Reisinger, Panpan Ren, Wolfgang Stockinger

Institutions: Tianjin University, University of Oxford, City University of Hong Kong

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G5432973176