Deep Learning for Mean-Field Systems with Common Noise

39 Pages Posted: 31 Aug 2024

See all articles by Nacira Agram

Nacira Agram

Royal Institute of Technology (KTH)

Jan Rems

University of Ljubljana

Abstract

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.

Keywords: McKean-Vlasov jump diffusion, signatures, common noise, deep learning

Suggested Citation

Agram, Nacira and Rems, Jan, Deep Learning for Mean-Field Systems with Common Noise. Available at SSRN: https://ssrn.com/abstract=4942172 or http://dx.doi.org/10.2139/ssrn.4942172

Nacira Agram (Contact Author)

Royal Institute of Technology (KTH) ( email )

Stockholm

Jan Rems

University of Ljubljana ( email )

Dunajska 104
Ljubljana, 1000
Slovenia

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