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Related papers: Doubly Reflected BSDEs in the predictable setting

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This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on the law of the solution. These reflected equations have been introduced recently by…

Probability · Mathematics 2020-08-26 Philippe Briand , Paul-Éric Chaudru de Raynal , Arnaud Guillin , Céline Labart

To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting…

Probability · Mathematics 2021-10-26 Feng-Yu Wang

This paper introduces a backward stochastic differential equation driven by both Brownian motion and a Markov chain (BSDEBM). Regime-switching is also incorporated through its driver. The existence and uniqueness of the solution of the…

Probability · Mathematics 2022-03-08 Engel John C. Dela Vega , Robert J. Elliott

We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form…

Probability · Mathematics 2026-01-23 Luca Di Persio , Matteo Garbelli , Adrian Zalinescu

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…

Probability · Mathematics 2020-09-09 Yunwen Wang , Jinfeng Li

The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori…

Probability · Mathematics 2021-11-17 Peng Luo , Mengbo Zhu

We consider a robust impulse control problem in finite horizon where the underlying uncertainty stems from an impulsively and continuously controlled functional stochastic differential equation (FSDE) driven by Brownian motion. We assume…

Optimization and Control · Mathematics 2021-03-31 Magnus Perninge

We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…

Probability · Mathematics 2014-11-11 Leszek Slominski

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

We consider a backward stochastic differential equation with a generator that can be subjected to delay, in the sense that its current value depends on the weighted past values of the solutions, for instance a distorted recent average.…

Probability · Mathematics 2015-09-08 Peng Luo , Ludovic Tangpi

This paper considers the problem of uniqueness of the solutions to a class of Markovian backward stochastic differential equations (BSDEs) which are also connected to certain nonlinear partial differential equation (PDE) through a…

Probability · Mathematics 2012-11-06 Coskun Cetin

In this paper, we consider a class of backward doubly stochastic differential equations (BDSDE for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the…

Probability · Mathematics 2017-02-06 Yaozhong Hu , David Nualart , Xiaoming Song

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…

Probability · Mathematics 2021-11-16 Yuyang Chen , Peng Luo

The theory of backward SDEs extends the predictable representation property of Brownian motion to the nonlinear framework, thus providing a path-dependent analog of fully nonlinear parabolic PDEs. In this paper, we consider backward SDEs,…

Probability · Mathematics 2022-02-14 Zhenjie Ren , Nizar Touzi , Junjian Yang

In this paper, we study the well-posedness of the Forward-Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the…

Probability · Mathematics 2015-06-30 Jin Ma , Zhen Wu , Detao Zhang , Jianfeng Zhang

In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part $M$ of a solution. We assume that the nonlinear term is merely monotone…

Probability · Mathematics 2023-08-22 Tomasz Klimsiak , Maurycy Rzymowski

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…

Probability · Mathematics 2021-06-15 Çağın Ararat , Jin Ma , Wenqian Wu

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

We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context of optimal control and optimal stopping problems. Motivated…

Optimization and Control · Mathematics 2025-11-05 Compoint Arthur , Sauldubois Nathan , Touzi Nizar

The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…

Numerical Analysis · Mathematics 2018-05-29 Richard Archibald , Feng Bao , Peter Maksymovych