arXiv:1109.5971 [math.AP]AbstractReferencesReviewsResources
On viscosity solutions of path dependent PDEs
Ibrahim Ekren, Christian Keller, Nizar Touzi, Jianfeng Zhang
Published 2011-09-27, updated 2014-01-14Version 2
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].
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)
Journal: Annals of Probability 2014, Vol. 42, No. 1, 204-236
DOI: 10.1214/12-AOP788
Keywords: viscosity solutions, path dependent pdes, path dependent semi-linear parabolic pdes, well-known nonlinear feynman-kac formula, non-markovian backward sdes
Tags: journal article
Related articles: Most relevant | Search more
arXiv:1412.8495 [math.AP] (Published 2014-12-29)
Viscosity Solutions of Path-dependent Integro-differential Equations
arXiv:1408.5267 [math.AP] (Published 2014-08-22)
An overview of Viscosity Solutions of Path-Dependent PDEs
arXiv:1511.02184 [math.AP] (Published 2015-11-06)
Moduli of Continuity for Viscosity Solutions