A discretization scheme for path-dependent FBSDEs and PDEs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912616139456512 |
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| author | Jang, Jiuk Park, Hyungbin |
| author_facet | Jang, Jiuk Park, Hyungbin |
| contents | This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key contribution of our approach is a novel estimator for the martingale integrand in the FBSDE, specifically designed to handle path-dependence more reliably than existing methods. We derive a concentration inequality that quantifies the statistical error of this estimator in a Monte Carlo framework. Based on these results, we investigate a supervised learning method with neural networks for solving path-dependent PDEs. The proposed algorithm is fully implementable and adaptable to a broad class of path-dependent problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07029 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A discretization scheme for path-dependent FBSDEs and PDEs Jang, Jiuk Park, Hyungbin Probability Computational Finance Mathematical Finance This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key contribution of our approach is a novel estimator for the martingale integrand in the FBSDE, specifically designed to handle path-dependence more reliably than existing methods. We derive a concentration inequality that quantifies the statistical error of this estimator in a Monte Carlo framework. Based on these results, we investigate a supervised learning method with neural networks for solving path-dependent PDEs. The proposed algorithm is fully implementable and adaptable to a broad class of path-dependent problems. |
| title | A discretization scheme for path-dependent FBSDEs and PDEs |
| topic | Probability Computational Finance Mathematical Finance |
| url | https://arxiv.org/abs/2308.07029 |