Open Access
January 2014 On viscosity solutions of path dependent PDEs
Ibrahim Ekren, Christian Keller, Nizar Touzi, Jianfeng Zhang
Ann. Probab. 42(1): 204-236 (January 2014). DOI: 10.1214/12-AOP788


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. "On viscosity solutions of path dependent PDEs." Ann. Probab. 42 (1) 204 - 236, January 2014.


Published: January 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1320.35154
MathSciNet: MR3161485
Digital Object Identifier: 10.1214/12-AOP788

Primary: 35D40 , 35K10 , 60H10 , 60H30

Keywords: Backward SDEs , Comparison principle , functional Itô formula , path dependent PDEs , viscosity solutions

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • January 2014
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