On viscosity solutions of path dependent PDEs
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Publication:2438749
DOI10.1214/12-AOP788zbMATH Open1320.35154arXiv1109.5971MaRDI QIDQ2438749
Author name not available (Why is that?)
Publication date: 6 March 2014
Published in: (Search for Journal in Brave)
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 It^{o} calculus recently introduced by Dupire [Functional It^{o} calculus (2009) Preprint].
Full work available at URL: https://arxiv.org/abs/1109.5971
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