Deep learning for conditional McKean-Vlasov jump diffusions

Agram, Nacira (author), Rems, Jan (author)

The current paper focuses on using deep learning methods to optimize the control of conditional McKean-Vlasov jump diffusions. We begin by exploring the dynamics of multi-particle jump-diffusion and presenting the propagation of chaos. The optimal control problem in the context of conditional McKean-Vlasov jump-diffusion is introduced along with the verification theorem (HJB equation). A linear quadratic conditional mean-field (LQ CMF) is discussed to illustrate these theoretical concepts. Then, we introduce a deep-learning algorithm that combines neural networks for optimization with path signatures for conditional expectation estimation. The algorithm is applied to practical examples, including LQ CMF and interbank systemic risk, and we share the resulting numerical outcomes.

• Language: English
• Keywords: McKean-Vlasov jump diffusion, signatures, common noise, deep learning
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.07.2025
• Year: 2025
• Number of pages: 15 str.
• Numbering: Vol. 201, [article no.] 106100
• PID: 20.500.12556/RUL-169570
• UDC: 519.2:517.997
• ISSN on article: 0167-6911
• DOI: 10.1016/j.sysconle.2025.106100
• COBISS.SI-ID: 238288387
• Publication date in RUL: 04.06.2025

Record is a part of a journal

• Title: Systems & Control Letters
• Shortened title: Syst. control. lett.
• Publisher: Elsevier
• ISSN: 0167-6911
• COBISS.SI-ID: 15539973

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Projects

• Funder: Swedish Research Council
• Project number: 2020-04697

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0448
• Name: Stohastične metode in njihova uporaba