Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability
Bouchard, Bruno; Loeper, Grégoire; Tan, Xiaolu (2021-09), Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability. https://basepub.dauphine.psl.eu/handle/123456789/22026
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-03277963
Series titleCahiers du CEREMADE
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Mathematics [CUHK]
Abstract (EN)We introduce a notion of approximate viscosity solution for a class of nonlinear path-dependent PDEs (PPDEs), including the Hamilton-Jacobi-Bellman type equations. Existence, comparaison and stability results are established under fairly general conditions. It is also consistent with smooth solutions when the dimension is less or equal to two, or the non-linearity is concave in the second order space derivative. We finally investigate the regularity (in the sense of Dupire) of the solution to the PPDE.
Subjects / KeywordsPPDE
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