Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

Roxana Dumitrescu (1, 2, 3) , Céline Labart (1, 4)

1 MATHRISK - Mathematical Risk handling
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 CREST - Centre de Recherche en Économie et Statistique
4 LAMA - Laboratoire de Mathématiques

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.

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

Domaines: Probabilités [math.PR]

Roxana Dumitrescu, Céline Labart. Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles. 2015. ⟨hal-01114996v1⟩