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}
}