Viscosity solutions of fully nonlinear parabolic path dependent PDEs. I.
From MaRDI portal
Publication:282508
DOI10.1214/14-AOP999zbMATH Open1375.35250arXiv1210.0006OpenAlexW4230022934MaRDI QIDQ282508
Author name not available (Why is that?)
Publication date: 12 May 2016
Published in: (Search for Journal in Brave)
Abstract: The main objective of this paper and the accompanying one cite{ETZ2} is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work cite{EKTZ}, focused on the semilinear case, and is crucially based on the nonlinear optimal stopping problem analyzed in cite{ETZ0}. We prove that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property and a partial comparison result. The latter is a key step for the wellposedness results established in cite{ETZ2}. We also show that the value processes of path-dependent stochastic control problems are viscosity solutions of the corresponding path dependent dynamic programming equation.
Full work available at URL: https://arxiv.org/abs/1210.0006
No records found.
No records found.
This page was built for publication: Viscosity solutions of fully nonlinear parabolic path dependent PDEs. I.
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q282508)
