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RBSDEs with optional barriers: monotone approximation

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  • In this short note we consider reflected backward stochastic differential equations (RBSDEs) with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous. In this case, the barrier is represented as a nondecreasing limit of right continuous with left limit (RCLL) barriers. We combine some well-known existence results for RCLL barriers with comparison arguments for the control process to construct solutions. Finally, we highlight the connection of these RBSDEs with standard RCLL BSDEs.

    Mathematics Subject Classification: 60H10, 60G40.


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