  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.
