
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
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Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-03277963Date
2021-09Series title
Cahiers du CEREMADEPages
33
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Show full item recordAuthor(s)
Bouchard, BrunoCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Grégoire
Tan, Xiaolu
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 / Keywords
PPDERelated items
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