Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911773849812992 |
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| author | Sun, Hui Bao, Feng |
| author_facet | Sun, Hui Bao, Feng |
| contents | We report two methods for solving FBSDEs of path dependent types of high dimensions. Specifically, we propose a deep learning framework for solving such problems using path signatures as underlying features. Our two methods (forward/backward) demonstrate comparable/better accuracy and efficiency compared to the state of the art techniques. More importantly, we are able to solve the problem of high dimension which is a limitation in the conventional methods. We also provide convergence proof for both methods with the proof of the backward methods in the Markovian case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06042 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing Sun, Hui Bao, Feng Probability We report two methods for solving FBSDEs of path dependent types of high dimensions. Specifically, we propose a deep learning framework for solving such problems using path signatures as underlying features. Our two methods (forward/backward) demonstrate comparable/better accuracy and efficiency compared to the state of the art techniques. More importantly, we are able to solve the problem of high dimension which is a limitation in the conventional methods. We also provide convergence proof for both methods with the proof of the backward methods in the Markovian case. |
| title | Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing |
| topic | Probability |
| url | https://arxiv.org/abs/2402.06042 |