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Pré-Publication, Document De Travail Année : 2023

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

Résumé

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.
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Dates et versions

hal-03277963 , version 1 (05-07-2021)
hal-03277963 , version 2 (07-09-2021)

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Bruno Bouchard, Grégoire Loeper, Xiaolu Tan. Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability. 2021. ⟨hal-03277963v2⟩
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