Work

On modified Euler methods for McKean–Vlasov stochastic differential equations with super-linear coefficients

Year: 2025

Type: article

Abstract: We introduce a new class of numerical methods for solving McKean–Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the drift and diffusion coefficients. Under certain non-globally Lipschitz conditions, the proposed numerical approaches have half-order convergence in the strong sense to the corresponding system of interacting particles associated with McKean–Vlasov SDEs. By leveraging a result on the propagation of chaos, we establish the full convergence rate of the modified Euler approximations to the solution of the McKean–Vlasov SDEs. Numerical experiments are included to validate the theoretical results.

Source: Automatica

DOI: 10.1016/j.automatica.2025.112284

Authors: Jiamin Jian, Qingshuo Song, Xiaojie Wang, Zhongqiang Zhang, Yuying Zhao

Institutions: University of Michigan, Worcester Polytechnic Institute, Central South University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,760

Funders: National Science Foundation, National Natural Science Foundation of China