English

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

Probability 2025-11-27 v2

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.

Keywords

Cite

@article{arxiv.2209.06097,
  title  = {Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations},
  author = {Luca Di Persio and Matteo Garbelli and Adrian Zălinescu},
  journal= {arXiv preprint arXiv:2209.06097},
  year   = {2025}
}