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arXiv · 2306.14615

Reflections on BSDEs

Dylan Possamaï·Marco Rodrigues
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Abstract

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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Dylan Possamaï, Marco Rodrigues. 2023-06-26. Reflections on BSDEs. https://doi.org/10.1214/24-ejp1123

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