\(\mathbb{L}^2\)-solutions for reflected BSDEs with jumps under monotonicity and general growth conditions: a penalization method. (English) Zbl 1420.60067
Summary: In this paper, we study generalized reflected backward stochastic differential equations with a càdlàg barrier, in a general filtration that supports a Brownian motion and an independent Poisson random measure. We give necessary and sufficient conditions for existence and uniqueness of \(\mathbb{L}^2\)-solutions for equations with generators monotone in \(y\). We also prove that the solutions can be approximated via the penalization method. Furthermore, a comparison theorem is provided for such equations.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
Keywords:
reflected backward stochastic differential equation; general filtration; jumps; penalization methodReferences:
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