Abstract
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.
Highlights
Let F = (Ft)t≥0 be a filtration satisfying the usual conditions and T be an arbitrary F-stopping time
We consider as given an FT measurable random variable ξ, a real function f defined on Ω×R+ ×R, which is F-progressively measurable with respect to the first two variables, and F-optional processes L, U of class (D) satisfying some separation condition
We consider reflected backward stochastic differential equations (RBSDE for short) which informally can be written in the form dYt = −f (t, Yt) dt − dRt + dMt on [0, T ]
Summary
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 L2-data and Lipschitz continuous generator were studied in [30] (Brownian filtration), in [13, 14, 31] (Brownian-Poisson filtration) and [3, 4, 15] (general filtration). In the present paper we study the existence and uniqueness of solutions of class (D) to RBSDEs (1.1) with general filtration F and possibly infinite terminal time T. In this case R is an increasing process.
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