Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles. (English) Zbl 1329.60234
Summary: We introduce a discrete time reflected scheme to solve doubly reflected backward stochastic differential equations with jumps (in short DRBSDEs) driven by a Brownian motion and an independent compensated Poisson process. As in [R. Dumitrescu and C. Labart, “Numerical approximation of doubly reflected BSDEs with jumps and RCLL obstacles” (2014)], we approximate the Brownian motion and the Poisson process by two random walks, but contrary to this paper, we discretize directly the DRBSDE, without using a penalization step. This gives us a fully implementable scheme, which only depends on one parameter of approximation: the number of time steps \(n\) (contrary to the scheme proposed in [loc. cit.], which also depends on the penalization parameter). We prove the convergence of the scheme, and give some numerical examples.
MSC:
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J75 | Jump processes (MSC2010) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |
Keywords:
doubly reflected backward stochastic differential equations; jumps; RCLL obstacles; numerical schemeReferences:
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