Related papers: Mean-Field Backward Stochastic Differential Equati…

Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely…

In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a…

In this paper we investigate mean-field backward doubly stochastic differential equations (BDSDEs), i.e., BDSDEs whose driving coefficients also depend on the joint law of the solution process as well as the solution of an associated…

Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a…

In this study, we concern the multidimensional viscosity solutions theory of a kind of semi-linear partial differential equations (PDEs). A new definition of viscosity solution for this multidimensional semi-linear PDEs which is related to…

In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure. Translating the splitting method introduced by Buckdahn, Li, Peng and Rainer [6]…

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 focus on the mean-field backward stochastic differential equations (BSDEs) driven by a fractional Brownian motion with Hurst parameter H greater then 1/2. First, the existence and uniqueness of these equations are…

We introduce a class of backward stochastic differential equations (BSDEs) on the Wasserstein space of probability measures. This formulation extends the classical correspondence between BSDEs, stochastic control, and partial differential…

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for…

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 paper, we study the backward stochastic differential equation (BSDE) with two nonlinear mean reflections, which means that the constraints are imposed on the distribution of the solution but not on its paths. Based on the backward…

(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay…

A backward stochastic differential equation (BSDE) is an SDE of the form $-dY_t = f(t,Y_t,Z_t)dt - Z_t^*dW_t;\ Y_T = \xi$. The subject of BSDEs has seen extensive attention since their introduction in the linear case by Bismut (1973) and in…

This paper is concerned with a backward-forward stochastic differential equation (BFSDE) system, in which a large number of negligible agents are coupled in their dynamics via state average. Here some BSDE is introduced as the dynamics of…

This paper investigates a class of generalized mean-reflected McKean-Vlasov type backward stochastic differential equations (BSDEs). Our new framework combines a mean reflection constraint on the solution's expectation with a generalized…

The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the…

In this paper, we introduce a new type of backward stochastic differential equations (BSDEs), called conditional expectation BSDEs, whose drivers depend not only on the value of the solutions but also on their conditional expectations with…

We consider backward stochastic differential equations (BSDEs) with mean-field and McKean-Vlasov interactions in their generators in a general setting, where the drivers are square-integrable martingales, with a focus on the independent…

This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs for short) with an unbounded terminal condition. Our results are deeply linked…