Related papers: $L^p$ solution of backward stochastic differential…
The aim of this paper is to derive a maximum principle for a control problem governed by a stochastic partial differential equation (SPDE) with locally monotone coefficients. In particular, necessary conditions for optimality for this…
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…
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…
We deduce conditional $L_p$-estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the…
In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between $L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{1}}) \otimes…
It is well-known that decision-making problems from stochastic control can be formulated by means of a forward-backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. 2022 proposed an efficient deep learning…
We discuss a class of Backward Stochastic Differential Equations(BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be associated…
We investigate solutions of backward stochastic differential equations (BSDE) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Levy process. In this new type of…
The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when the…
In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation…
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a…
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in…
In this paper, by introducing a new notion of envelope of the stochastic process, we construct a family of random differential equations whose solutions can be viewed as solutions of a family of ordinary differential equations and prove…
In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique…
This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…
We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival…
We extend the work of Delong and Imkeller (2010a,b) concerning Backward stochastic differential equations with time delayed generators (delay BSDE). We give moment and a priori estimates in general $L^p$-spaces and provide sufficient…
In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of…
In this paper we present a unified approach to establish gradient type formulas and Bismut type formulas for backward stochastic differential equations (BSDEs). This approach relies on a mix of derivative formulas with respect to the…
In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…