Related papers: General Existence Results for Reflected BSDE and B…

In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…

In this paper, we deal with Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in [3]. We extend the recent work [2] of…

We consider systems of backward stochastic differential equations with c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces…

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…

We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the…

In this paper, we first establish the existence and uniqueness of $L^p\ (p>1)$ solutions for multidimensional backward stochastic differential equations (BSDEs) under a weak monotonicity condition together with a general growth condition in…

We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators singular in $ y $. First, we establish the existence of solutions and a comparison theorem, thereby extending results in the literature.…

This paper is intended to give a representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized…

In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz…

This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…

We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations…

This paper addresses reflected backward stochastic differential equations (RBSDE hereafter) that take the form of \begin{eqnarray*} \begin{cases} dY_t=f(t,Y_t, Z_t)d(t\wedge\tau)+Z_tdW_t^{\tau}+dM_t-dK_t,\quad Y_{\tau}=\xi, Y\geq…

In this paper, we establish representation theorems for generators of backward stochastic differential equations (BSDEs in short), whose generators are monotonic and convex growth in $y$ and quadratic growth in $z$. We also obtain a…

This paper investigates $L^{1}$ solutions for mean-field backward stochastic differential equations (MFBSDEs) under different weak assumptions in both one-dimensional and multi-dimensional settings, whose generator $f(\omega,t,y,z,\mu)$…

We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a…

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…

With the terminal value $|\xi|$ admitting some given exponential moment, we put forward and prove several existence and uniqueness results for the unbounded solutions of quadratic backward stochastic differential equations whose generators…

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 consider Backward Stochastic Differential Equations (BSDE) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition and the generator to depend on a vector…

This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use it connection with…