APPROXIMATE VISCOSITY SOLUTIONS OF PATH-DEPENDENT PDES AND DUPIRE'S VERTICAL DIFFERENTIABILITY
成果类型：
Article
署名作者：
Bouchard, Bruno; Loeper, Gregoire; Tan, Xiaolu
署名单位：
Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Monash University; Monash University; Chinese University of Hong Kong
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/23-AAP1960
发表日期：
2023
页码：
5781-5809
关键词：
摘要：
We introduce a notion of approximate viscosity solutions for a class of nonlinear path-dependent PDEs (PPDEs), including the Hamilton-Jacobi- Bellman-type equations. Existence, comparaison and stability results have been established under fairly general conditions. It is also consistent with the notion of smooth solution when the dimension is less or equal to two, or the nonlinearity is concave in the second order space derivative. We finally investigate the regularity (in the sense of Dupire) of the solution to the PPDE.