Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918300140699648 |
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| author | Di Persio, Luca Garbelli, Matteo Zalinescu, Adrian |
| author_facet | Di Persio, Luca Garbelli, Matteo Zalinescu, Adrian |
| contents | We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form of a Generalized BSDE. We establish the connection between this FBSDE system and non-linear path-dependent PDEs with Neumann boundary conditions by deriving a representation formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs Di Persio, Luca Garbelli, Matteo Zalinescu, Adrian Probability 60H10, 60H30, 35R15, 35K20 We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form of a Generalized BSDE. We establish the connection between this FBSDE system and non-linear path-dependent PDEs with Neumann boundary conditions by deriving a representation formula. |
| title | Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs |
| topic | Probability 60H10, 60H30, 35R15, 35K20 |
| url | https://arxiv.org/abs/2601.16178 |