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In this paper we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type: \[Y_t=\xi -\int_{t\wedge \tau}^{\tau}Y_r|Y_r|^q dr-\int_{t\wedge \tau}^{\tau}Z_r dB_r,\qquad t\geq 0,\]…

Probability · Mathematics 2009-09-29 A. Popier

The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and…

Probability · Mathematics 2007-05-23 Fabrice Blache

In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. The…

Probability · Mathematics 2011-09-12 S. Hamadene , Y. Ouknine

We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…

Probability · Mathematics 2007-05-23 Thomas Muller-Gronbach

In this article we extend the exact simulation methods of Beskos et al. to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we…

Probability · Mathematics 2013-01-15 Pierre Etore , Miguel Martinez

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

Statistical Mechanics · Physics 2011-10-11 P. L. Krapivsky , J. M. Luck , K. Mallick

In this paper, we consider forward-backward stochastic differential equation driven by $G$-Brownian motion ($G$-FBSDEs in short) with small parameter $\varepsilon > 0$. We study the asymptotic behavior of the solution of the backward…

Probability · Mathematics 2020-03-27 Ibrahim Dakaou , Abdoulaye Soumana Hima

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

In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and…

Probability · Mathematics 2025-05-01 Li Tan , Shengrong Wang

This paper considers the setting governed by $(\mathbb{F},\tau)$, where $\mathbb{F}$ is the "public" flow of information, and $\tau$ is a random time which might not be $\mathbb{F}$-observable. This framework covers credit risk theory and…

Probability · Mathematics 2024-08-12 T. Choulli , S. Alsheyab

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

We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution…

Probability · Mathematics 2016-08-14 Idris Kharroubi , Jin Ma , Huyên Pham , Jianfeng Zhang

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just…

Probability · Mathematics 2017-11-23 Imen Hassairi

In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stochastically monotone with respect to the drift parameter. In…

Probability · Mathematics 2025-06-05 Xi Geng , Greg Markowsky

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

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…

Probability · Mathematics 2021-03-17 Tianyang Nie , Marek Rutkowski

In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model, but not driven by Brownian motion, and give existence and uniqueness results for the…

Probability · Mathematics 2015-05-14 Dimbinirina Ramarimbahoaka , Zhe Yang , Robert J. Elliott

We introduce a generalized notion of semilinear elliptic partial differential equations where the corresponding second order partial differential operator $L$ has a generalized drift. We investigate existence and uniqueness of generalized…

Probability · Mathematics 2015-06-03 Francesco Russo , Lukas Wurzer

We solve a class of BSDE with a power function $f(y) = y^q$, $q > 1$, driving its drift and with the terminal boundary condition $ \xi = \infty \cdot \mathbf{1}_{B(m,r)^c}$ (for which $q > 2$ is assumed) or $ \xi = \infty \cdot…

Probability · Mathematics 2016-11-29 Ali Devin Sezer , Thomas Kruse , Alexandre Popier

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