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The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not…

Optimization and Control · Mathematics 2012-05-28 Liangquan Zhang , Yufeng Shi

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…

Probability · Mathematics 2015-07-21 Shiqiu Zheng , Shoumei Li

This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…

Probability · Mathematics 2015-08-12 ShengJun Fan

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple $(Y,Z,\psi)$ where $Y$ is a semimartingale, and $(Z,\psi)$ are the diffusion and jump…

Mathematical Finance · Quantitative Finance 2018-07-10 Masaaki Fujii , Akihiko Takahashi

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…

Computational Finance · Quantitative Finance 2014-12-23 Masaaki Fujii

We introduce a domination argument which asserts that: if we can dominate theparameters of a quadratic backward stochastic differential equation (QBSDE) with continuousgenerator from above and from below by those of two BSDEs having ordered…

Probability · Mathematics 2019-03-28 Khaled Bahlali

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 show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a…

Probability · Mathematics 2019-11-21 Dirk Becherer , Martin Büttner , Klebert Kentia

We consider a class of Backward Stochastic Differential Equations with superlinear driver process $f$ adapted to a filtration supporting at least a $d$ dimensional Brownian motion and a Poisson random measure on ${\mathbb R}^m- \{0\}.$ We…

Probability · Mathematics 2019-11-19 Mahdi Ahmadi , Alexandre Popier , Ali Devin Sezer

This paper extends the domination-monotonicity conditions, which guarantee the well-posedness of extended mean-filed forward-backward stochastic differential equations (extended MF-FBSDEs), from the previously studied linear framework to a…

Optimization and Control · Mathematics 2026-05-12 Hao Wu

In this paper, by virtue of Malliavin calculus, we establish a relationship between backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs, and thus extend the well-known nonlinear…

Probability · Mathematics 2018-10-17 Jiaqiang Wen , Yufeng Shi

In this paper, we study a class of Quadratic Backward Stochastic Differential Equations (QBSDE in short) with jumps and unbounded terminal condition. We extend the class of quadratic semimartingales introduced by Barrieu and El Karoui…

Probability · Mathematics 2016-03-22 Nicole El Karoui , Anis Matoussi , Armand Ngoupeyou

In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…

Systems and Control · Computer Science 2020-06-18 Ioannis Exarchos , Evangelos A. Theodorou

We study the small-time local controllability (STLC) of a bilinear Schr\"odinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case where the linearized system is not controllable, necessitating…

Analysis of PDEs · Mathematics 2025-09-09 Karine Beauchard , Frédéric Marbach , Thomas Perrin

In this paper, we study one-dimensional backward stochastic differential equation with jump under logarithmic growth assumption in the z-variable (|z|\sqrt{|\ln|z|}|) and an L^p terminal value (for a suitable p>2). We show the existence and…

Probability · Mathematics 2021-03-17 Khalid Oufdil

We prove an existence and uniqueness result for two-obstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic…

Probability · Mathematics 2020-12-08 Laurent Denis , Anis Matoussi , Jing Zhang

This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…

Optimization and Control · Mathematics 2016-10-11 Maoning Tang , Qingxin Meng

Hu et. al 2018 studied a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. By assuming a weakly coupled condition, they established an approach to obtain the…

Optimization and Control · Mathematics 2018-12-31 Mingshang Hu , Shaolin Ji , Xiaole Xue

Using purely probabilistic methods, we prove the existence and the uniqueness of solutions fora system of coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous coefficients. As a…

Probability · Mathematics 2021-10-12 Kihun Nam , Yunxi Xu

In this paper, we analyze the mean field backward stochastic differential equations (MFBSDEs) with double mean reflections, whose generator and constraints both depend on the distribution of the solution. When the generator is Lipschitz…

Probability · Mathematics 2026-01-12 Hanwu Li , Jin Shi