A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with Lévy jumps

Agarwal, A. and Pagliarani, S. (2021) A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with Lévy jumps. Stochastics, 93(4), pp. 592-624. (doi: 10.1080/17442508.2020.1771337)

[img] Text
215023.pdf - Accepted Version



We consider a class of Lévy-driven stochastic differential equations (SDEs) with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed that the coefficient is bounded, affine in the state variable, and only measurable in the law of the solution. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration scheme that approximates the law of the solution through its characteristic function. Numerical illustrations show the effectiveness of our method, which appears to be appropriate to handle the multi-dimensional setting.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Agarwal, Dr Ankush
Authors: Agarwal, A., and Pagliarani, S.
Subjects:Q Science > QA Mathematics
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Stochastics
Publisher:Taylor & Francis
ISSN (Online):1744-2516
Published Online:08 June 2020
Copyright Holders:Copyright © 2020 Informa UK Limited, trading as Taylor and Francis Group
First Published:First published in Stochastics 93(4): 592-624
Publisher Policy:Reproduced in accordance with the publisher copyright policy
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record