An Euler scheme for BSDEs via the Wiener chaos decomposition
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909968754540544 |
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| author | Lozano, Pere Díaz Di Nunno, Giulia |
| author_facet | Lozano, Pere Díaz Di Nunno, Giulia |
| contents | The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener chaos decomposition to approximate these quantities. In contrast to many numerical schemes that rely on a forward-backward (Markovian) structure, our approach accommodates arbitrary $\mathcal{F}_T$-measurable square-integrable terminal conditions. We provide a comprehensive convergence analysis and illustrate the method on several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Euler scheme for BSDEs via the Wiener chaos decomposition Lozano, Pere Díaz Di Nunno, Giulia Numerical Analysis Probability 65C30, 60H35, 60H07, 65C05, 65G99 The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener chaos decomposition to approximate these quantities. In contrast to many numerical schemes that rely on a forward-backward (Markovian) structure, our approach accommodates arbitrary $\mathcal{F}_T$-measurable square-integrable terminal conditions. We provide a comprehensive convergence analysis and illustrate the method on several numerical examples. |
| title | An Euler scheme for BSDEs via the Wiener chaos decomposition |
| topic | Numerical Analysis Probability 65C30, 60H35, 60H07, 65C05, 65G99 |
| url | https://arxiv.org/abs/2512.16418 |