Related papers: BSDEs driven by G-Brownian motion with time-varyin…
Distribution dependent stochastic differential equations have been a very hot subject with extensive studies. On the other hand, under the $G$-expectation framework, stochastic differential equations driven by $G$-Brownian motion (in short…
In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected…
In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward…
In this paper, we consider a reflected backward stochastic differential equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing quadratically in the second unknown. We obtain the existence by the penalty method, and…
Our aim is to study the well-posedness of quasilinear stochastic partial differential equations driven by G-Brownian motion (GSPDEs for short) and the associated backward doubly stochastic differential equations (GBDSDEs for short). We…
In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion (RGBSDE for short). The reflection keeps the solution above a given stochastic process. In order to…
In this note, we prove that if $g$ is uniformly continuous in $z$, uniformly with respect to $(\oo,t)$ and independent of $y$, the solution to the backward stochastic differential equation (BSDE) with generator $g$ is unique.
We investigate solutions of backward stochastic differential equations (BSDE) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Levy process. In this new type of…
In this paper, we study the discrete-time approximation schemes for a class of backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) which corresponds to the hedging pricing of European contingent claims. By…
In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic…
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…
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…
In this paper, we study the numerical method for solving forward-backward stochastic differential equations driven by $G$-Brownian motion ($G$-FBSDEs) which correspond to fully nonlinear partial differential equations (PDEs). First, we give…
In this paper, we study the existence and uniqueness of solutions to the fully coupled nonlinear forward-backward stochastic differential equations driven by G-Brownian motion. Assuming that the diffusion coefficient $\sigma$ is uniformly…
This paper discusses a new type of anticipated backward stochastic differential equation with a time-delayed generator (DABSDEs, for short) driven by fractional Brownian motion, also known as fractional BSDEs, with Hurst parameter…
In this paper, we prove that there exists at least one solution for the reflected forward-backward stochastic differential equation driven by G-Brownian motion satisfying the obstacle constraint with monotone coefficients.
In this paper we are concerned with distribution dependent backward stochastic differential equations (DDBSDEs) driven by Gaussian processes. We first show the existence and uniqueness of solutions to this type of equations. This is done by…
In this paper, we consider forward-backward stochastic differential equation driven by $G$-Brownian motion ($G$-FBSDEs in short) with small parameter $\varepsilon > 0$. We study the asymptotic behavior of the solution of the backward…
The present paper considers a new kind of backward stochastic differential equations driven by G-Brownian motion, which is called ergodic G-BSDEs. Firstly, the well-posedness of G-BSDEs with infinite horizon is given by a new linearization…
In this paper, we study the reflected stochastic differential equations driven by G-Brownian motion (reflected G-SDEs) with two nonlinear constraints. With the help of the Skorokhod problem with nonlinear constraints, we first study the…