On viscosity solutions of path dependent PDEs
Analysis of PDEs
2014-01-15 v2 Functional Analysis
Probability
Abstract
In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional It\^{o} calculus recently introduced by Dupire [Functional It\^{o} calculus (2009) Preprint].
Cite
@article{arxiv.1109.5971,
title = {On viscosity solutions of path dependent PDEs},
author = {Ibrahim Ekren and Christian Keller and Nizar Touzi and Jianfeng Zhang},
journal= {arXiv preprint arXiv:1109.5971},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP788 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)