Related papers: Some results on general quadratic reflected BSDEs …
In this paper, we study the uniqueness of the solution of reflected BSDE with one or two barriers, under continuous and linear increasing condition of generator $g$. Before that we study the construction of solution of of reflected BSDE…
We deal with a class of fully coupled forward-backward stochastic differential equations (FBSDE for short), driven by Teugels martingales associated with some L\'evy process. Under some assumptions on the derivatives of the coefficients, we…
The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when the…
For general mean-field backward stochastic differential equations (BSDEs) it is well-known that we usually do not have the comparison theorem if the coefficients depend on the law of $Z$-component of the solution process $(Y, Z)$. A natural…
The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and…
We discuss BSDE with drivers containing nonlinearities of the type $p(y)|z|$ and $p(y)|z|^2$ with $p$ a polynomial of any degree. Sufficient conditions are given for existence and uniqueness of solutions as well as comparison results. We…
We establish some well-posedness and comparison results for BSDEs driven by one- and multi-dimensional martingales. On the one hand, our approach is largely motivated by results and methods developed in Carbone et al. (2008) and El Karoui…
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…
We study generalized backward stochastic differential equations (BSDEs) up to a random time horizon $\vartheta$, which is not a stopping time, under minimal assumptions regarding the properties of $\vartheta$. In contrast to existing works…
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…
In this paper, we continue in solving reflected generalized backward stochastic differential equations (RGBSDE for short) and fixed terminal time with use some new technical aspects of the stochastic calculus related to the reflected…
We formulate a notion of doubly reflected BSDEs with a default time and two completely separated RCLL barriers. We demonstrate the existence and uniqueness of the solution. Within the defaultable setup, we introduce a type of generalized…
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 the existence and uniqueness of $\mathbb{L}^p$-solutions for $p \in (1, 2)$, first for backward stochastic differential equations (BSDEs) in a general filtration that supports a Brownian motion and an independent…
We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption and with a general filtration. Under a technical assumption (a Mokobodzki-type condition), we show…
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…
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…
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the…
We show existence and uniqueness of solutions to BSDEs of the form $$ Y_t = \xi + \int_t^T f(s,Y_s,Z_s)ds - \int_t^T Z_s dW_s$$ in the case where the terminal condition $\xi$ has bounded Malliavin derivative. The driver $f(s,y,z)$ is…
This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to $z$ and bounded terminal conditions. We first study a slight…