Reflected generalized discontinuous BSDEs with rcll barrier and an obstacle problem of IPDE with nonlinear Neumann boundary conditions
Volume 10, Issue 1 (2023), pp. 77–110
Pub. online: 30 December 2022
Type: Research Article
Open Access
Open Access
Received
2 July 2022
2 July 2022
Revised
12 October 2022
12 October 2022
Accepted
12 December 2022
12 December 2022
Published
30 December 2022
30 December 2022
Abstract
Reflected generalized backward stochastic differential equations (BSDEs) with one discontinuous barrier are investigated when the noise is driven by a Brownian motion and an independent Poisson measure. The existence and uniqueness of the solution are derived when the generators are monotone and the barrier is right-continuous with left limits (rcll). The link is established between this solution and a viscosity solution for an obstacle problem of integral-partial differential equations with nonlinear Neumann boundary conditions.
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