Non-Continuous Double Barrier Reflected BSDES With Jumps under a Stochastic Lipschitz Coefficient

Abstract

We consider a doubly reflected backward stochastic differential equations with jumps where the lower barrier and the opposite of the upper barrier are assumed to be right upper-semicontinuous (not necessarily càdlàg). We provide existence and uniqueness result when the coefficient is stochastic Lipschitz by using an equivalent transformation which is a coupled system of one-reflected backward stochastic differential equations.

Nonlinear BSDEs with two optional Doob's class barriers satisfying weak Mokobodzki's condition and extended Dynkin games

“…Results on optional barriers, L 1 -data and possibly infinite horizon time were presented in [25]. The case of L 2 -data and f being stochastic Lipschitz driver was presented in [29] (Brownian-Poisson filtration) and in [28,31] (general filtration).…”

Reflected BSDEs with two optional barriers and monotone coefficient on general filtered space

“…In most of the existing papers on RBSDEs càdlàg barriers are considered, and there are only few papers dealing with non-càdlàg case. Such equations with L 2 -data and Lipschitz continuous generator were studied in [30] (Brownian filtration), in [13,14,31] (Brownian-Poisson filtration) and [3,4,15] (general filtration). RBSDEs with L 1 -data and optional barriers were considered only in [25,26] in case of Brownian filtration and bounded terminal time.…”

Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

“…To this direction, several attempts have been done. Among others, we refer to [4,5,9,15,[21][22][23][24] for the case of BSDEs, and [16,25,26,30] for BDSDEs. In our paper, we use a generalization of the Doob-Meyer decomposition called the Mertens decomposition.…”

“…To this direction, several attempts have been done. Among others, we refer to [4,5,9,15,[21][22][23][24] for the case of BSDEs, and [16,25,26,30] for BDSDEs.…”