A Discretization Scheme for BSDEs with Random Time Horizon
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912468802994176 |
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| author | Seifried, Frank T. Würschmidt, Maximilian |
| author_facet | Seifried, Frank T. Würschmidt, Maximilian |
| contents | We analyze a natural extension of the backward Euler approximation for a class of BSDEs with Lipschitz generators and random (unbounded) time horizons. We derive strong error bounds in terms of the underlying stepsize; the distance between the continuous terminal time and a discrete-time approximation; the distance between the terminal condition and a respective approximation; and an integrated distance depending on an approximation of the time component of the generator - all are scaled by the exponential of the maximal terminal time. As application we consider decoupled FBSDEs on bounded domains. We use an Euler-Maruyama scheme to approximate the diffusion and further refine our error bounds to only depend on the distance of the exit times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Discretization Scheme for BSDEs with Random Time Horizon Seifried, Frank T. Würschmidt, Maximilian Probability Numerical Analysis 60H10, 60G40, 65N75 G.1.8; G.3 We analyze a natural extension of the backward Euler approximation for a class of BSDEs with Lipschitz generators and random (unbounded) time horizons. We derive strong error bounds in terms of the underlying stepsize; the distance between the continuous terminal time and a discrete-time approximation; the distance between the terminal condition and a respective approximation; and an integrated distance depending on an approximation of the time component of the generator - all are scaled by the exponential of the maximal terminal time. As application we consider decoupled FBSDEs on bounded domains. We use an Euler-Maruyama scheme to approximate the diffusion and further refine our error bounds to only depend on the distance of the exit times. |
| title | A Discretization Scheme for BSDEs with Random Time Horizon |
| topic | Probability Numerical Analysis 60H10, 60G40, 65N75 G.1.8; G.3 |
| url | https://arxiv.org/abs/2507.04882 |