Related papers: Lp-solution of backward doubly stochastic differen…

In this paper backward stochastic differential equations with interaction (shorter BSDEs with interaction) are introduced. Far to our knowledge, this type of equation is not seen in the literature before. Existence and uniqueness result for…

This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…

In this paper, we study the doubly conditional reflected backward stochastic differential equations (BSDEs), where constraints are made on the conditional expectation of the first component of the solution with respect to a general…

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in the previous work. In other words we do not need to require the uniform exponential decay of the…

In this paper, we study the solvability problem for one kind of fully coupled forward-backward stochastic difference equations (FBS{\Delta}Es). With the help of the necessary and sufficient condition for the solvability of the linear…

This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.

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 this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…

We introduce a new class of Backward Stochastic Differential Equations in which the $T$-terminal value $Y_{T}$ of the solution $(Y,Z)$ is not fixed as a random variable, but only satisfies a weak constraint of the form $E[\Psi(Y_{T})]\ge…

In this paper, we consider a stochastic decision problem for a system governed by a stochastic differential equation, in which an optimal decision is made in such a way to minimize a vector-valued accumulated cost over a finite-time horizon…

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…

In this paper, we present a backward deep BSDE method applied to Forward Backward Stochastic Differential Equations (FBSDE) with given terminal condition at maturity that time-steps the BSDE backwards. We present an application of this…

This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate…

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of…

In this article, we propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator,…

This work deals with the numerical approximation of backward stochastic differential equations (BSDEs). We propose a new algorithm which is based on the regression-later approach and the least squares Monte Carlo method. We give some…

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…

This thesis consists of three parts. In the first part, we study $\mathbb{L}^p$ solutions of a large class of BSDEs. Existence, comparison theorem, uniqueness and a stability result are proved. In the second part, we establish the…

In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous,…

This paper is concerned with solution in H\"{o}lder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as…