@article{a375781562524191a14361fd35ae2d51,
title = "Comparison of viscosity solutions of fully nonlinear degenerate parabolic path-dependent PDEs",
abstract = "We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi, and Zhang [Ann. Probab., 44 (2016), pp. 2507{2553], our conditions are easier to check and allow for the degenerate case, thus including first order path-dependent PDEs. Our argument follows the reg- ularization method as introduced by Jensen, Lions, and Souganidis [Proc. Amer. Math. Soc., 102, (1988)] in the corresponding finite-dimensional PDE setting. The present argument significantly sim-plifies the comparison proof of Ekren, Touzi, and Zhang but requires an Lp-type of continuity (with respect to the path) for the viscosity semisolutions and for the nonlinearity defining the equation.",
keywords = "Comparison principle, Path-dependent PDEs, Regularization, Viscosity solutions",
author = "Zhenjie Ren and Nizar Touzi and Jianfeng Zhang",
note = "Funding Information: ∗Received by the editors August 19, 2016; accepted for publication (in revised form) May 3, 2017; published electronically October 24, 2017. http://www.siam.org/journals/sima/49-5/M109033.html Funding: The second author was supported by ANR, the Chair Financial Risks of the Risk Foundation sponsored by Soci{\'e}t{\'e}G{\'e}n{\'e}rale, and the Chair Finance and Sustainable Development sponsored by EDF and Calyon. The third author was supported in part by NSF grant DMS 1413717. †Universit{\'e}Paris–Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016 Paris, France (ren@ceremade.dauphine.fr). ‡CMAP, Ecole Polytechnique, Paris, France (nizar.touzi@polytechnique.edu). §Department of Mathematics, University of Southern California, Los Angeles, CA 90089 (jianfenz@usc.edu). Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",
year = "2017",
doi = "10.1137/16M1090338",
language = "English (US)",
volume = "49",
pages = "4093--4116",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",
}