Related papers: Minimal Supersolutions of Convex BSDEs under Const…
We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower…
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…
We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the…
We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space…
In the present article we provide existence, uniqueness and stability results under an exponential moments condition for quadratic semimartingale backward stochastic differential equations (BSDEs) having convex generators. We show that the…
We consider the minimal super-solution of a backward stochastic differential equation with constraint on the gains-process. The terminal condition is given by a function of the terminal value of a forward stochastic differential equation.…
We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely,…
In this paper we prove some uniqueness results for quadratic backward stochastic differential equations without any convexity assumptions on the generator. The bounded case is revisited while some new results are obtained in the unbounded…
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…
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…
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 introduce a domination argument which asserts that: if we can dominate theparameters of a quadratic backward stochastic differential equation (QBSDE) with continuousgenerator from above and from below by those of two BSDEs having ordered…
We study the existence of minimal supersolutions of BSDEs under a family of mutually singular probability measures. We consider generators that are jointly lower semicontinuous, positive, and either convex in the control variable and…
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 provide existence results and comparison principles for solutions of backward stochastic difference equations (BS$\Delta$Es) and then prove convergence of these to solutions of backward stochastic differential equations (BSDEs) when the…
In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the…
We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator $g$ may be non-Lipschitz continuous in the state variable $y$,…
We deal with backward stochastic differential equations with time delayed generators. In this new type of equations, a generator at time t can depend on the values of a solution in the past, weighted with a time delay function for instance…
We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in…
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…