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In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153…

Probability · Mathematics 2015-09-10 Nabil Kazi-Tani , Dylan Possamaï , Chao Zhou

This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…

Probability · Mathematics 2019-02-26 Shiqiu Zheng , Gaofeng Zong

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…

Probability · Mathematics 2022-06-06 Antonis Papapantoleon , Dylan Possamai , Alexandros Saplaouras

In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points…

Numerical Analysis · Mathematics 2018-08-09 Chol-Kyu Pak , Mun-Chol Kim , O Hun

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

Numerical Analysis · Mathematics 2014-01-21 Siqing Gan , Aiguo Xiao , Desheng Wang

In this paper we obtain results for the existence and uniqueness of solutions to coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps defined on a random environment. This environment corresponds to a…

Probability · Mathematics 2024-01-19 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

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…

Probability · Mathematics 2023-12-13 Weiye Yang

Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs).…

Probability · Mathematics 2014-12-17 Stefan Engblom

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…

Probability · Mathematics 2021-05-17 Anna Aksamit , Libo Li , Marek Rutkowski

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…

Probability · Mathematics 2026-05-12 Ruisen Qian

In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if $(W^n)$ is a sequence of…

Probability · Mathematics 2007-05-23 Sandrine Toldo

In this paper we obtain a comparison theorem for backward stochastic partial differential equation (SPDEs) with jumps. We apply it to introduce space-dependent convex risk measures as a model for risk in large systems of interacting…

Probability · Mathematics 2014-02-19 Bernt Øksendal , Agnès Sulem , Tusheng Zhang

In this paper, we study a kind of constrained backward stochastic differential equations (BSDEs) such that the nonlinear expectation of the composition of a loss function and the solution remains above zero. The existence and uniqueness…

Probability · Mathematics 2025-11-24 Hanwu Li

The purpose of the present paper is to introduce and establish a notion of stability for the backward propagation of chaos with respect to (initial) data sets. Consider, for example, a sequence of discrete-time martingales converging to a…

Probability · Mathematics 2025-09-30 Antonis Papapantoleon , Alexandros Saplaouras , Stefanos Theodorakopoulos

In this paper, a class of stable explicit $\theta$-schemes are proposed for solving anticipated backward stochastic differential equations (anticipated BSDEs) which generator not only contains the present values of the solutions but also…

Numerical Analysis · Mathematics 2024-09-23 Mingshang Hu , Lianzi Jiang

In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…

Probability · Mathematics 2024-01-12 Jiahao Liang , Shanjian Tang

In this paper, we consider the stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps. First, under certain averaging conditions, we are able to show that the solutions of…

Probability · Mathematics 2023-08-07 Guangjun Shen , Jie Xiang , Jiang-Lun Wu

In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…

Probability · Mathematics 2007-11-21 Rainer Buckdahn , Juan Li , Shige Peng

In this paper we study backward stochastic differential equations (BSDEs) driven by the compensated random measure associated to a given pure jump Markov process X on a general state space K. We apply these results to prove well-posedness…

Probability · Mathematics 2013-02-05 Fulvia Confortola , Marco Fuhrman

In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present…

Probability · Mathematics 2014-06-30 Shige Peng , Zhe Yang