BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. (English) Zbl 1337.60123
Stochastics 88, No. 4, 491-539 (2016); corrections ibid. 89, No. 8, 1201-1227 (2018).
Summary: We analyze multidimensional BSDEs in a filtration that supports a Brownian motion and a Poisson random measure. Under a monotonicity assumption on the driver, the paper extends several results from the literature. We establish existence and uniqueness of solutions in \(L^p\) provided that the generator and the terminal condition satisfy appropriate integrability conditions. The analysis is first carried out under a deterministic time horizon, and then generalized to random time horizons given by a stopping time with respect to the underlying filtration. Moreover, we provide a comparison principle in dimension one.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J65 | Brownian motion |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 60G57 | Random measures |
Keywords:
backward stochastic differential equations; Brownian motion; Poisson random measure; jumps; general filtrationReferences:
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