On Viscosity Solutions of Path Dependent Pdes

  title={On Viscosity Solutions of Path Dependent Pdes},
  author={Christian Keller and Nizar Touzi},
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… CONTINUE READING
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