Deep Learning for solving Fokker-Planck-Kolmogorov Equation Arising from Jump-Diffusion Model

The Fokker-Planck-Kolmogorov (FPK) equation generated by the jump-diffusion model is represented as a Partial Integro-Differential Equation (PIDE). Traditional numerical methods for solving PIDEs are often constrained by dimensionality and the complexity of mesh generation. To address these limitations, this paper proposes a novel deep-learning approach for solving PIDEs. Building upon the existing Physics-Informed Neural Network (PINN) framework for solving Partial Differential Equations (PDEs), we incorporate additional deep neural networks (DNNs) and construct a novel loss function to simultaneously optimize the integral terms and the solution for approximating the PIDE. The results demonstrate that our approach accurately captures the system's dynamic behaviour, highlighting its effectiveness and potential for solving complex PIDEs.