Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

Dumitrescu, Roxana; Labart, Céline

Dumitrescu, Roxana; Labart, Céline (2016), Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles, Journal of Computational and Applied Mathematics, 296, p. 827-839. 10.1016/j.cam.2015.11.006

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1502.02888v2

Date

2016

Journal name

Journal of Computational and Applied Mathematics

Volume

296

Publisher

Elsevier

Published in

Paris

Pages

827-839

Abstract (EN)

We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differ-ential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independentcompensated Poisson process. As in [5], we approximate the Brownian motion and the Poisson processby two random walks, but contrary to this paper, we discretize directly the DRBSDE, without using apenalization step. This gives us a fully implementable scheme, which only depends on one parameter ofapproximation: the number of time stepsn(contrary to the scheme proposed in [5], which also dependson the penalization parameter). We prove the convergence of the scheme, and give some numericalexamples.

Subjects / Keywords

numerical scheme; Backward stochastic differential equations with jumps; Double barrier reflected BSDEs