Related papers: A new comparison theorem of multidimensional BSDEs
Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the…
In this paper, we study conditions under which the solutions of a backward stochastic differential equation with jump remains in a given set of constrains. This property is the so-called "viability property". As an application, we study the…
For backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison…
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 establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in $z$. As some applications, we obtain a general converse comparison…
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…
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 establishes a new existence and uniqueness result of solutions for multidimensional backward stochastic differential equations (BSDEs) whose generators satisfy a weak monotonicity condition and a general growth condition in $y$,…
In this paper, we study multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs which is established recently in [14], we…
A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with…
Our previous results are extended to the case of the margin account, which may depend on the contract's value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman (1995), Mercurio (2013) and…
Suppose $N$ is a compact Riemannian manifold, in this paper we will introduce the definition of $N$-valued BSDE and $L^2(\mathbb{T}^m;N)$-valued BSDE for which the solution are not necessarily staying in only one local coordinate. Moreover,…
In this paper, we establish representation theorems for generators of backward stochastic differential equations (BSDEs in short) in probability spaces with general filtration from the perspective of transposition solutions of BSDEs. As…
In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or…
We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the…
In this paper, we introduce a new type of backward stochastic differential equations (BSDEs) with infinite anticipation, where the generator depends on the entire future values of the solution in infinite horizon. We show that the new BSDEs…
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…
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows (with respect to both unknown variables $y$ and $z$) in a…
Results on the existence, uniqueness and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are established. The goal is to develop a general multi-asset framework encompassing a wide spectrum of…
Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochastic control, financial technology and machine learning. In…