Reflections on BSDEs
We prove well-posedness results for backward stochastic differential equations (BSDEs) and reflected BSDEs with an optional obstacle process in the case of appropriately weighted \(\mathbb{L}^2\)-data when the generator is integrated with respect to a possibly purely discontinuous process. This lead...
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Veröffentlicht in: | arXiv.org 2024-12 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | We prove well-posedness results for backward stochastic differential equations (BSDEs) and reflected BSDEs with an optional obstacle process in the case of appropriately weighted \(\mathbb{L}^2\)-data when the generator is integrated with respect to a possibly purely discontinuous process. This leads to a unified treatment of discrete-time and continuous-time (reflected) BSDEs. We compare our well-posedness results with the current literature and highlight that our results are sharp and cannot be improved within the framework presented here. Finally, we provide sufficient conditions for a comparison principle. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.2306.14615 |