Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability

Bouchard, Bruno; Loeper, Grégoire; Tan, Xiaolu

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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Document de travail / Working paper

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https://hal.archives-ouvertes.fr/hal-03277963

Date

2021-09

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Cahiers du CEREMADE

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Auteur(s)

Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Grégoire
Tan, Xiaolu
Department of Mathematics [CUHK]

Résumé (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.