Related papers: Doubly Reflected BSDEs with default time under sto…
We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle $L$ and the upper obstacle $U$ of the equation are completely separated, we…
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…
We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption and with a general filtration. Under a technical assumption (a Mokobodzki-type condition), we show…
We introduce a generalized Dynkin game problem with non linear conditional expectation ${\cal E}$ induced by a Backward Stochastic Differential Equation (BSDE) with jumps. Let $\xi, \zeta$ be two RCLL adapted processes with $\xi \leq…
In this paper, we study the doubly conditional reflected backward stochastic differential equations (BSDEs), where constraints are made on the conditional expectation of the first component of the solution with respect to a general…
The aim of this paper is twofold. First, we extend the results of [33] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar…
We consider a reflected backward stochastic differential equations with default time and an optional barrier in a filtration generated by a one-dimensional Brownian motion and a defaultable process. We suppose that the barrier have…
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…
We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we…
In this paper, we want to investigate some kind of Dynkin's game under ambiguity which is represented by Backward Stochastic Differential Equation (shortly BSDE) with standard generator function g(t, y, z). Under regular assumptions, a pair…
In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous,…
We study reflected backward stochastic differential equation (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of the paper lies in fact that we consider the following weak assumptions on the data: barriers…
We study the existence of a solution for a one-dimensional generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under assumptions on the input data which are weaker than that on the current…
In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale…
This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.
In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on $y$, with Lipschitz condition on $z$.
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…
We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time $t$ can depend on the values of a solution in the…
We are interested on reflected advanced backward stochastic differential equations (RABSDE) with default. By the predictable representation property and for a Lipschitz driver, we show that the RABSDE with default has a unique solution in…
In this paper, we continue in solving reflected generalized backward stochastic differential equations (RGBSDE for short) and fixed terminal time with use some new technical aspects of the stochastic calculus related to the reflected…