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

Abstract

We consider a system of Forward Backward Stochastic Differential Equations (FBSDEs), with time delayed generator and driven by L\`evy-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.