Related papers: A general existence and uniqueness result on multi…
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 establish a general existence and uniqueness result of $L^1$ solution for a multidimensional backward stochastic differential equation (BSDE for short) with generator $g$ satisfying a one-sided Osgood condition as well as a general…
This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…
In this paper, we study the multi-dimensional mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. Under small terminal value, the existence and uniqueness are proved for the multi-dimensional…
By imposing an additional integrability condition on the first component of the solution, this paper establishes an existence and uniqueness result for $L^1$ solutions of multidimensional backward stochastic differential equations (BSDEs)…
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…
In this paper, we study the well-posedness of backward doubly stochastic differential equations (BDSDEs), both with and without reflection, under weak conditions. First, when the generator $f$ is of general growth in $y$ and linear growth…
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 present a unified approach to $L^p$-solutions ($p > 1$) of multidimensional backward stochastic differential equations (BSDEs) driven by L\'evy processes and more general filtrations. New existence, uniqueness and comparison results are…
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of one-dimensional backward stochastic differential equations (BSDEs) with sub-quadratic generators, where the terminal time is allowed to be…
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator $g$ satisfies a weak…
This paper investigate a class of multi-dimensional backward stochastic differential equations (BSDEs) with singualr generators exhibiting diagonally quadratic growth and unbounded terminal conditions, thereby extending results in the…
This paper is devoted to the $L^p$ ($p>1$) solutions of one-dimensional backward stochastic differential equations (BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in $t$ and $\omega$. An…
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 first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…
This study focuses on a multidimensional backward stochastic differential equation (BSDE) with a general random terminal time $\tau$ taking values in $[0,+\infty]$. The generator $g$ satisfies a stochastic monotonicity condition in the…
Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochastic control, financial technology and machine learning. In…
This paper is devoted to a general solvability of a multi-dimensional backward stochastic differential equation (BSDE) of a diagonally quadratic generator $g(t,y,z)$, by relaxing the assumptions of \citet{HuTang2016SPA} on the generator and…
In this paper, we study multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs which is established recently in [14], we…
In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator, which is of…