Jan Rems: Deep Learning for Conditional McKean-Vlasov Jump Diffusions

Abstract

This talk focuses on using deep learning methods to optimize the control of conditional McKean-Vlasov jump-diffusions. We will 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 will be introduced along with the verification theorem (HJB equation). Practical examples will be 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 will be applied to practical examples, and we will share the resulting numerical outcomes. Based on joint work with Nacira Agram (KTH).