Related papers: General time interval multidimensional BSDEs with …

In a recent paper, Soner, Touzi and Zhang [20] have introduced a notion of second order backward stochastic differential equations (2BSDEs for short), which are naturally linked to a class of fully non-linear PDEs. They proved existence and…

We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs the Stieltjes integral with respect to an increasing…

This paper is devoted to a general solvability of multi-dimensional non-Markovian backward stochastic differential equations (BSDEs) with interactively quadratic generators. Some general structures of the generator $g$ are posed for both…

In this paper, we study backward stochastic differential equations driven by G-Brownian motion where the generator has time-varying monotonicity with respect to y and Lipsitz property with respect to z. Through the Yosida approximation, we…

In this paper, we study a collection of mean-reflected backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs), where $G$-expectations are constrained in some time-dependent intervals. To establish…

In this paper, we focus on the solvability of a class of fractional backward stochastic differential equations (BSDEs, for short) with delayed generator. In this class of equations, the generator includes not only the values of the…

We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness…

In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear…

This paper aims at solving a one-dimensional backward stochastic differential equation (BSDE for short) with only integrable parameters. We first establish the existence of a minimal $L^1$ solution for the BSDE when the generator $g$ is…

In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random…

This paper investigates McKean-Vlasov backward stochastic variational inequalities (BSVIs) whose generator depends on the joint law of the solution. We first establish the existence and uniqueness of the solution under globally Lipschitz…

The paper is concerned with adapted solution of a multi-dimensional BSDE with a "diagonally" quadratic generator, the quadratic part of whose $i$th component only depends on the $i$th row of the second unknown variable. Local and global…

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 study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a…

This paper is devoted to the study of the differentiability of solutions to real-valued backward stochastic differential equations (BSDEs for short) with quadratic generators driven by a cylindrical Wiener process. The main novelty of this…

We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a time-dependent extended…

In this paper, we establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in $z$. As some applications, we obtain a general converse comparison…

With the terminal value $\xi^-$ admitting a certain exponential moment and $\xi^+$ admitting every exponential moments or being bounded, we establish several existence and uniqueness results for unbounded solutions of backward stochastic…

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 consider the backward stochastic differential equation (BSDE) with generator $f(y)|z|^2,$ where the function $f$ is defined on an open interval $D$ and locally integrable. The existence and uniqueness of bounded solutions…