A note on optional Snell envelopes and reflected backward SDEs

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).…”

Penalization method for reflected BDSDEs with two-sided jumps and driven by Lévy process

“…Recently, Berrhazi et al [8] considered RBDSDEs when the barrier is not necessarily right-continuous by inspiring on the work of Grigorova et al [15] which is the first one dealing with right upper semicontinuous barrier reflected BSDEs. For more developments on Reflected BSDEs when the barrier is not necessarily right-continuous, we refer to [1,6,16,19,23,25,26]. More recently, Marzougue and Sagna [27] extended the work of Berrhazi et al [8] to the case when the noise is driven also by an independent Poisson random measure under the so-called stochastic Lipschitz condition on the drivers.…”

Reflected and Doubly RBSDEs with Irregular Obstacles and a Large Set of Stopping Strategies

“…In the case of a non-rightcontinuous process ξ, this optimal stopping problem has been studied in [28, p. 136], where the assumption of right-continuity of ξ was replaced by the weaker assumption of right-uppersemicontinuity (r.u.s.c.). Recently, Marzougue [24] considered a formulation of problem (1.1) closest to ours, where the reward is a ladlag positive process. Using the definition of split stopping times given in [25], he studied the following problem: For each stopping time θ,…”