Abstract
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.
Funding Statement
The research of Xiaolu Tan is supported by CUHK startup grant and Hong Kong RGC General Research Fund (Project 14302622 and Project 14302921).
Citation
Bruno Bouchard. Grégoire Loeper. Xiaolu Tan. "Approximate viscosity solutions of path-dependent PDEs and Dupire’s vertical differentiability." Ann. Appl. Probab. 33 (6B) 5781 - 5809, December 2023. https://doi.org/10.1214/23-AAP1960
Information