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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…

Probability · Mathematics 2010-06-08 Yufeng Shi , Qingfeng Zhu

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…

Probability · Mathematics 2020-03-03 Yinggu Chen , Boualem Djehiche , Said Hamadene

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.

Probability · Mathematics 2008-02-06 Guangyan Jia

In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be…

Probability · Mathematics 2017-03-28 Patrick Cheridito , Kihun Nam

We introduce and develop the concepts of Geometric Backward Stochastic Differential Equations (GBSDEs, for short) and two-driver BSDEs. We demonstrate their natural suitability for modeling continuous-time dynamic return risk measures. We…

Probability · Mathematics 2025-09-10 Roger J. A. Laeven , Emanuela Rosazza Gianin , Marco Zullino

In a first step, we establish the existence (and sometimes the uniqueness) of solutions for a large class of quadratic backward stochastic differential equations (QBSDEs) with continuous generator and a merely square integrable terminal…

Probability · Mathematics 2014-07-15 Khaled Bahlali , M'hamed Eddahbi , Youssef Ouknine

We study a backward stochastic differential equation whose terminal condition is an integrable function of a local martingale and generator has bounded growth in $z$. When the local martingale is a strict local martingale, the BSDE admits…

Probability · Mathematics 2011-12-13 Hao Xing

In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with sub-differential operators that are driven by infinite-dimensional martingales which involve symmetry, that is, the process involves a positive…

Probability · Mathematics 2023-06-06 Pei Zhang , Adriana Irawati Nur Ibrahim , Nur Anisah Mohamed

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The…

Numerical Analysis · Mathematics 2013-11-26 M. V. Tretyakov , Z. Zhang

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…

Probability · Mathematics 2017-05-30 Jiaqiang Wen , Yufeng Shi

In this paper, we study the backward stochastic differential equations driven by G-Brownian motion under the condition that the generator is time-varying Lipschitz continuous with respect to y and time-varying uniformly continuous with…

Probability · Mathematics 2024-09-26 Bingru Zhao

The present paper is devoted to the study of mean-field backward stochastic differential equations (MFBSDEs) with double mean reflections whose generators are not Lipschitz continuous. With the help of the Skorokhod problem and some a…

Probability · Mathematics 2025-10-14 Li Hanwu , Shi Jin

We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a time-dependent extended…

Probability · Mathematics 2019-01-21 Christel Geiss , Alexander Steinicke

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness…

Probability · Mathematics 2008-12-10 Marie-Amelie Morlais

In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques,…

Probability · Mathematics 2017-01-17 Lishun Xiao , Shengjun Fan

In this paper, we study one-dimensional backward stochastic differential equation (BSDE, for short), whose coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. In addition, if the terminal condition $\xi$ has bounded Malliavin…

Probability · Mathematics 2022-08-09 Yufeng Shi , Zhi Yang

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

Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217,…

Probability · Mathematics 2010-08-03 Joscha Diehl , Peter Friz

In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via…

Probability · Mathematics 2025-08-27 Wei He , Qiangjun Tang

In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the…

Probability · Mathematics 2012-06-04 Na Zhang , Guangyan Jia