An Overview of Viscosity Solutions of Path-Dependent PDEs
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Publication:5374169
DOI10.1007/978-3-319-11292-3_15zbMATH Open1384.35042arXiv1408.5267OpenAlexW2118626917MaRDI QIDQ5374169
Author name not available (Why is that?)
Publication date: 9 April 2018
Published in: (Search for Journal in Brave)
Abstract: This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12].
Full work available at URL: https://arxiv.org/abs/1408.5267
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