Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles
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
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1502.02888v2
Journal nameJournal of Computational and Applied Mathematics
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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 , 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 , which also dependson the penalization parameter). We prove the convergence of the scheme, and give some numericalexamples.
Subjects / Keywordsnumerical scheme; Backward stochastic differential equations with jumps; Double barrier reflected BSDEs
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