Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866917104092971008 |
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| author | Di Persio, Luca Garbelli, Matteo Zălinescu, Adrian |
| author_facet | Di Persio, Luca Garbelli, Matteo Zălinescu, Adrian |
| contents | We consider a system of Forward Backward Stochastic Differential Equations (FBSDEs), with time delayed generator and driven by Lèvy-type noise. We establish a non linear Feynman Kac representation formula associating the solution given by the FBSDEs-system to the solution of a path dependent nonlinear Kolmogorov equation with both delay and jumps. Obtained results are then applied to study a generalization of the so-called Large Investor Problem where the stock price evolves according to a jump-diffusion dynamic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_06097 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations Di Persio, Luca Garbelli, Matteo Zălinescu, Adrian Probability 34K50, 60H15, 60G51, 60H30 We consider a system of Forward Backward Stochastic Differential Equations (FBSDEs), with time delayed generator and driven by Lèvy-type noise. We establish a non linear Feynman Kac representation formula associating the solution given by the FBSDEs-system to the solution of a path dependent nonlinear Kolmogorov equation with both delay and jumps. Obtained results are then applied to study a generalization of the so-called Large Investor Problem where the stock price evolves according to a jump-diffusion dynamic. |
| title | Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations |
| topic | Probability 34K50, 60H15, 60G51, 60H30 |
| url | https://arxiv.org/abs/2209.06097 |