Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

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• 作者：Roxana Dumitrescu^a ; ^b ; ^c ; ^{roxana@ceremade.dauphine.fr" class="auth_mail" title="E-mail the corresponding author} ; Cé ; line Labart^d ; ^c ; ^{celine.labart@univ-savoie.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60H10 ; 60H35 ; 60J75 ; 34K28
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：827-839
• 全文大小：476 K

文摘

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 Dumitrescu and Labart (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$n$ (contrary to the scheme proposed in Dumitrescu and Labart (2014), which also depends on the penalization parameter). We prove the convergence of the scheme, and give some numerical examples.