Related papers: Mean-Field Doubly Reflected Backward Stochastic Di…
This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a…
The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations (BSDE) and…
We study the problem of existence and uniqueness of solutions of backward stochastic differential equations with two reflecting irregular barriers, $L^p$ data and generators satisfying weak integrability conditions. We deal with equations…
We consider a one-reflected backward stochastic differential equation with a general RCLL barrier in a filtration that supports a Brownian motion and an independent Poisson random measure. We establish the existence and uniqueness of a…
In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a comparison theorem establish here for…
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…
We consider backward stochastic differential equations (BSDEs) with mean-field and McKean-Vlasov interactions in their generators in a general setting, where the drivers are square-integrable martingales, with a focus on the independent…
This paper studies a system of multi-dimensional reflected backward stochastic differential equations with oblique reflections (RBSDEs for short) in infinite horizon associated to switching problems. The existence and uniqueness of the…
The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the…
In this paper, we are concerned with the problem of existence of solutions for generalized reflected backward stochastic differential equations (GRBSDEs for short) and generalized backward stochastic differential equations (GBSDEs for…
We prove existence and uniqueness of solutions of reflected backward stochastic differential equations in time-dependent adapted and c\`adl\`ag convex regions $\mathcal{D}=\{D_t;t\in[0,T]\}$. We also show that the solution may be…
In this paper, we study a kind of constrained backward stochastic differential equations (BSDEs) such that the nonlinear expectation of the composition of a loss function and the solution remains above zero. The existence and uniqueness…
In this paper, we study the existence and uniqueness of $\mathbb{L}^p$-solutions for $p \in (1, 2)$, first for backward stochastic differential equations (BSDEs) in a general filtration that supports a Brownian motion and an independent…
Under a generalized Mokobodzki condition for reflected BSDEs with two continuous barriers which relates the growth of the generator $g$ and that of the barriers, we establish several existence and uniqueness results on $L^p\ (p>1)$…
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 aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs,…
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 discrete-time approximation of multidimensional reflected BSDEs of the type of those presented by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89-121] and generalized by Hamad\`ene and Zhang [Stochastic…
We establish sufficient conditions for the existence and uniqueness of mean-field backward stochastic differential equations with time delayed generator in the sense that at t, the generator may depend on previous values up to a delay…
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.…