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

TL;DR

This paper extends the Feynman-Kac formula to FBSDEs with jumps and delays, linking solutions to path-dependent nonlinear Kolmogorov equations, and applies it to a large investor problem with jump-diffusion stock dynamics.

Contribution

It introduces a novel Feynman-Kac representation for FBSDEs with delays and jumps, connecting them to path-dependent PDEs with practical financial applications.

Findings

Established a nonlinear Feynman-Kac formula for delayed FBSDEs with jumps.

Linked solutions of FBSDEs to path-dependent nonlinear Kolmogorov equations.

Applied results to a large investor problem with jump-diffusion stock prices.

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.