Related papers: Doubly Reflected BSDEs in the predictable setting
We introduce a new formulation of reflected BSDEs and doubly reflected BSDEs associated with irregular obstacles. In the first part of the paper, we consider an extension of the classical optimal stopping problem over a larger set of…
In this short note we consider RBSDE with Lipschitz drivers and barrier processes that are optional and right upper semicontinuous. We treat the case when the barrier can be represented as a decreasing limit of cadlag barriers. We combine…
We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independent compensated Poisson process. As in…
We consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon reflected BSDEs to the setting…
In this paper we study multi-dimensional reflected backward stochastic differential equations driven by Wiener-Poisson type processes. We prove existence and uniqueness of solutions, with reflection in the inward spatial normal direction,…
In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…
In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be…
We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators. Two methods, i.e., the penalization method and the Picard…
We introduce a new class of reflected backward stochastic differential equations with two c\`adl\`ag barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove…
In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. The…
A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with…
In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations with stochastic Lipschitz coefficient. We derive the existence and uniqueness of the solutions for those equations via Snell…
In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method.…
In this paper, an optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (RBSDEs, for short) where the generators, the terminal values and the barriers are all switched with positive…
In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator…
The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus…
We prove an existence and uniqueness result for two-obstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic…
In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via…
We establish several existence, uniqueness and comparison results for $L^1$ solutions of non-reflected BSDEs and reflected BSDEs with one and two continuous barriers under the assumption that the generator $g$ satisfies a one-sided Osgood…
We solve a class of doubly reflected backward stochastic differential equation whose generator depends on the resistance due to reflections, which extend the recent work of Qian and Xu on reflected BSDE with one barrier. We then obtain the…