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arXiv · 1109.5971

On viscosity solutions of path dependent PDEs

Ibrahim Ekren·Christian Keller·Nizar Touzi·Jianfeng Zhang
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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 Itô calculus recently introduced by Dupire [Functional Itô calculus (2009) Preprint].

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Ibrahim Ekren, Christian Keller, Nizar Touzi, Jianfeng Zhang. 2014-01-14. On viscosity solutions of path dependent PDEs. https://doi.org/10.1214/12-aop788

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