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Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

Abstract : 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-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 $n$ (contrary to the scheme proposed in Dumitrescu-Labart (2014), which also depends on the penalization parameter). We prove the convergence of the scheme, and give some numerical examples.
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Submitted on : Monday, November 9, 2015 - 3:44:38 PM
Last modification on : Friday, January 21, 2022 - 3:20:09 AM
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  • HAL Id : hal-01114996, version 2
  • ARXIV : 1502.02888

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Roxana Dumitrescu, Céline Labart. Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles. Journal of Computational and Applied Mathematics, Elsevier, 2016, 296, pp.827-839. ⟨hal-01114996v2⟩

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