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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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: 1744-2508
• 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

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