Viscosity Solutions of Path-Dependent PDEs and Non-Markovian Forward-Backward Stochastic Equations
Probability
2013-06-19 v4
Abstract
It is known that Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac representation formulae for semilinear parabolic PDEs. We show that non-Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac formulae for semilinear path-dependent PDEs. This extends the result proved in Ekren, Keller, Touzi, and Zhang [4] to the case with a possibly degenerate diffusion coefficient in the forward dynamics.
Keywords
Cite
@article{arxiv.1202.2502,
title = {Viscosity Solutions of Path-Dependent PDEs and Non-Markovian Forward-Backward Stochastic Equations},
author = {Andrea Cosso},
journal= {arXiv preprint arXiv:1202.2502},
year = {2013}
}