We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the solution may be approximated by a modified penalization method. Application to an optimal stopping problem is given. MSC 2000 subject classifications: primary 60H10; secondary 60G40.Keywords: Reflected backward stochastic differential equation, processes with regulated trajectories, modified penalization method, optimal stopping problem.M loc (resp. M) is the set of all F-martingales (resp. local martingales) M such that M 0 = 0. M p , p ≥ 1, denotes the space of all M ∈ M such that

We consider reflected backward stochastic differential equations with two optional barriers of class (D) satisfying Mokobodzki's separation condition, and coefficient which is only continuous and non-increasing. We assume that data are merely integrable and the terminal time is an arbitrary (possibly infinite) stopping time. We study the problem of the existence and uniqueness of solutions to the mentioned equations, and their connections with the value process in nonlinear Dynkin games.

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove the existence and uniqueness of L p solutions, p ≥ 1, and show that the solutions may be approximated by a modified penalization method.MSC 2000 subject classifications: Primary 60H10; secondary 60G40.

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