Feynman–Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations

We consider a system of forward backward stochastic differential equations (FBSDEs) with a time-delayed generator driven by Levy-type noise. We establish a non-linear Feynman-Kac representation formula associating the solution given by the FBSDEs system to the solution of a path dependent nonlinear Kolmogorov equation with both delay and jumps. Obtained results are then applied to study a generalization of the so-called large investor problem, where the stock price evolves according to a jump-diffusion dynamic.