Work

Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments

Year: 2024

Type: article

Abstract: We deduce stability and pathwise uniqueness for a McKean–Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz continuous drift and includes moment estimates for random Itô processes that are of independent interest. For deterministic coefficients, we provide unique strong solutions even if the drift fails to be of affine growth. The theory that we develop rests on Itô’s formula and leads to pth moment and pathwise exponential stability for $$p\ge 2$$ p ≥ 2 with explicit Lyapunov exponents.

Source: Journal of Theoretical Probability

DOI: 10.1007/s10959-024-01344-2

Authors: Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske

Institutions: Ludwig-Maximilians-Universität München, University of Oslo

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: $3,090

Funder: Ludwig-Maximilians-Universität München