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
Hauptverfasser: Possamaï, Dylan, Rodrigues, Marco
Format: Artikel
Sprache:eng
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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.
ISSN:2331-8422
DOI:10.48550/arxiv.2306.14615