Deep learning for conditional McKean-Vlasov Jump diffusions

39 Pages Posted: 12 Apr 2024

See all articles by Jan Rems

Jan Rems

University of Ljubljana

Nacira Agram

Royal Institute of Technology (KTH)

Date Written: March 15, 2024

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 and the verification theorem (HJB equation) are introduced. A linear quadratic conditional mean-field control 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 linear quadratic conditional mean-field control and interbank systemic risk, and we share the resulting numerical outcomes.

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

JEL Classification: C60, C61, C45

Suggested Citation

Rems, Jan and Agram, Nacira, Deep learning for conditional McKean-Vlasov Jump diffusions (March 15, 2024). Available at SSRN: https://ssrn.com/abstract=4760864 or http://dx.doi.org/10.2139/ssrn.4760864

Jan Rems (Contact Author)

University of Ljubljana ( email )

Dunajska 104
Ljubljana, 1000
Slovenia

Nacira Agram

Royal Institute of Technology (KTH) ( email )

Stockholm

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