Convergence rates for Backward SDEs driven by Lévy processes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911769716326400 |
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| author | Liu, Chenguang Papapantoleon, Antonis Saplaouras, Alexandros |
| author_facet | Liu, Chenguang Papapantoleon, Antonis Saplaouras, Alexandros |
| contents | We consider Lévy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by Lévy processes that are approximated by BSDEs driven by their compound Poisson approximations. We are interested in the rate of convergence of the approximate BSDEs to the ones driven by the Lévy processes. The rate of convergence of the Lévy processes depends on the Blumenthal--Getoor index of the process. We derive the rate of convergence for the BSDEs in the $\mathbb L^2$-norm and in the Wasserstein distance, and show that, in both cases, this equals the rate of convergence of the corresponding Lévy process, and thus is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rates for Backward SDEs driven by Lévy processes Liu, Chenguang Papapantoleon, Antonis Saplaouras, Alexandros Probability Optimization and Control Mathematical Finance 60G51, 91G60, 60G44, 60G42 We consider Lévy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by Lévy processes that are approximated by BSDEs driven by their compound Poisson approximations. We are interested in the rate of convergence of the approximate BSDEs to the ones driven by the Lévy processes. The rate of convergence of the Lévy processes depends on the Blumenthal--Getoor index of the process. We derive the rate of convergence for the BSDEs in the $\mathbb L^2$-norm and in the Wasserstein distance, and show that, in both cases, this equals the rate of convergence of the corresponding Lévy process, and thus is optimal. |
| title | Convergence rates for Backward SDEs driven by Lévy processes |
| topic | Probability Optimization and Control Mathematical Finance 60G51, 91G60, 60G44, 60G42 |
| url | https://arxiv.org/abs/2402.01337 |