BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula
Probability
2011-08-23 v1 Analysis of PDEs
Abstract
In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE are formulated through a classical backward stochastic differential equation (BSDEs, for short) in which the terminal values and the generators are allowed to be general functions of Brownian paths. In this way we have established a new type of nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of regularities for this new PDE was obtained.
Keywords
Cite
@article{arxiv.1108.4317,
title = {BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula},
author = {Shige Peng and Falei Wang},
journal= {arXiv preprint arXiv:1108.4317},
year = {2011}
}