Constrained Backward SDEs with Jumps: Application to Optimal Switching

Romuald Elie (1, 2) , Idris Kharroubi (1, 3)

1 CREST - Centre de Recherche en Économie et Statistique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we introduce a new class of BSDE generalizing and offering a unifying framework to represent the constrained ones presented in [16] or [12] as well as the oblique reflected ones studied by [11] and [9]. Via a penalization procedure, we provide an existence and uniqueness result for this new class of so-called constrained BSDEs with jumps. Remarkably, these BSDEs appear to be very convenient to represent the solution to eventually non-Markovian switching problems. As a by-product, we enlarge the class of obliquely reflected BSDE's, allowing to represent switching problems with controlled underlined diffusion.

Mots clés: Switching problems; BSDE with jumps; Constrained BSDE; Reflected BSDE

Domaines: Probabilités [math.PR]

Romuald Elie, Idris Kharroubi. Constrained Backward SDEs with Jumps: Application to Optimal Switching. 2009. ⟨hal-00369404v1⟩