Related papers: General time interval multidimensional BSDEs with …
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…
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…
Our aim is to study the following new type of multivalued backward stochastic differential equation: \[ \left\{\begin{array} [c]{r}-dY\left(t\right) +\partial\varphi\left(Y\left(t\right)\right) dt\ni…
We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…
In this paper, we study one-dimensional backward stochastic differential equation (BSDE, for short), whose coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. In addition, if the terminal condition $\xi$ has bounded Malliavin…
We study Backward Stochastic Differential Equations on a probability space equipped with a Brownian filtration. We assume that the terminal value and the generator at zero are merely integrable. Moreover, the generator is assumed to be…
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{\"o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the…
This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with sub-differential operators that are driven by infinite-dimensional martingales which involve symmetry, that is, the process involves a positive…
In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDE), whose generators are continuous with linear growth. It generalizes some known representation theorems…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
In this paper, we present martingale decomposition on time scales. We establish the related backward stochastic dynamic equations on time scales (this paper BS$\nabla$E for short, concerning $\nabla$-integral on time scales) which unify…
In this paper, we investigate the well-posedness of bounded and unbounded solutions for reflected backward stochastic differential equations (RBSDEs) and backward stochastic differential equations (BSDEs). The generators of these equations…
In this paper, we study multidimensional generalized BSDEs that have a monotone generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. First, we prove the existence and uniqueness of…
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 give necessary and sufficient condition for existence and uniqueness of $\mathbb{L}^{p}$-solutions of reflected BSDEs with continuous barrier, generator monotone with respect to $y$ and Lipschitz continuous with respect to $z$, and with…
In this paper we study a multidimensional quadratic BSDE with a particular class of product generators and give a result of existence of solution in a suitable complete metric space under some constraints on parameters. We also use that…
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 establish several existence, uniqueness and comparison results for $L^1$ solutions of non-reflected BSDEs and reflected BSDEs with one and two continuous barriers under the assumption that the generator $g$ satisfies a one-sided Osgood…
With an emphasis on generators with quadratic growth in the control variable we consider measure solutions of BSDE, a solution concept corresponding to the notion of risk neutral measure in mathematical finance. In terms of measure…