On viscosity solutions of path dependent PDES

Ibrahim Ekren, Christian Keller, Nizar Touzi, Jianfeng Zhang

Research output: Contribution to journalArticlepeer-review


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].

Original languageEnglish (US)
Pages (from-to)204-236
Number of pages33
JournalAnnals of Probability
Issue number1
StatePublished - Jan 2014


  • Backward SDEs
  • Comparison principle
  • Functional itô formula
  • Path dependent PDEs
  • Viscosity solutions

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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