2011/09/30 by Ibrahim Ekren, Christian Keller, Nizar Touzi +1 · 1 citation
Mathematics · #math.AP #math.FA #math.PR
paper · pdf · doi:10.1214/12-aop788
published as Annals of Probability 2014, Vol. 42, No. 1, 204-236 · 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)
arxiv created 2014/01/14 · arxiv updated 2014/01/15
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 Itô calculus recently introduced by Dupire [Functional Itô calculus (2009) Preprint].