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Publications (27)

math.PR2021

Invariant representation for generators of general time interval quadratic BSDEs under stochastic growth conditions

Guangshuo Zhou, Fengjiao Du, Shengjun Fan

This paper is devoted to proving a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator…

math.PR2024

On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions: the certain exponential moment case

Yan Wang, Yaqi Zhang, Shengjun Fan

With the terminal value $∣ I^¾∣$ admitting some given exponential moments, we propose and prove several existence and uniqueness results for the unbounded solutions of quadratic back…

math.PR2021

Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs

Shengjun Fan, Ying Hu, Shanjian Tang

This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows…

math.PR2024

Weighted $L^{p} (p \geq 1)$ solutions of random time horizon BSDEs with stochastic monotonicity generators

Xinying Li, Shengjun Fan

In this paper, we are concerned with a multidimensional backward stochastic differential equation (BSDE) with a general random terminal time $I ¨ $ , which may take values in $[0,+\in…

math.PR2026

Solvability of BSDEs with possibly unbounded stochastic coefficients on a general weighted $L^{p}$ space

Yaqi Zhang, Xinying Li, Ying Hu +1

This paper is devoted to solving a multidimensional backward stochastic differential equation (BSDE for short) with a general random terminal time $I ¨ $ taking values in $[0,+\infty…

math.PR2017

A representation theorem for generators of BSDEs with general growth generators in $y$ and its applications

Lishun Xiao, Shengjun Fan

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 invo…

math.PR2026

1D nonlinear backward stochastic differential equations: a unified theory and applications

Shengjun Fan, Ying Hu, Shanjian Tang

Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochas…

math.PR2025

Uniqueness of adapted solutions to scalar BSDEs with Peano-type generators

Shengjun Fan, Ying Hu, Shanjian Tang

A Backward Stochastic Differential Equation (BSDE) with a Peano-type generator, is known to have infinitely many solutions when the terminal value is vanishing, and is shown to hav…

math.PR2025

Unbounded Dynamic Concave Utilities via BSDEs

Shengjun Fan, Ying Hu, Shanjian Tang

The dynamic concave utility (or the dynamic convex risk measure) of an unbounded endowment is studied and represented as the value process in the unique solution of a backward stoc…

math.PR2019

General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition

Tingting Li, Ziheng Xu, Shengjun Fan

This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), whe…

math.PR2024

Weighted solutions of random time horizon BSDEs with stochastic monotonicity and general growth generators and related PDEs

Xinying Li, Yaqi Zhang, Shengjun Fan

This study focuses on a multidimensional backward stochastic differential equation (BSDE) with a general random terminal time $I ¨ $ taking values in $[0, + \infty]$ . The generator $g$ …

math.PR2021

$L^{p}$ solutions of doubly reflected BSDEs under general assumptions

Shengjun Fan, Qianyun Qian

Under a generalized Mokobodzki condition for reflected BSDEs with two continuous barriers which relates the growth of the generator $g$ and that of the barriers, we establish sever…

math.PR2024

Existence, uniqueness and comparison theorem on unbounded solutions of general time interval BSDEs with sub-quadratic generators

Chuang Gu, Yan Wang, Shengjun Fan

This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of one-dimensional backward stochastic differential equations (BSDEs) with sub-quad…

math.PR2013

$L^{p}$ $(p \geq 1)$ solutions of multidimensional BSDEs with monotone generators in general time intervals

Lishun Xiao, Shengjun Fan, Na Xu

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^{p}$ $(p \geq 1)$ . We first study the existence and…

math.PR2024

Multi-dimensional non-Markovian backward stochastic differential equations of interactively quadratic generators

Shengjun Fan, Ying Hu, Shanjian Tang

This paper is devoted to a general solvability of multi-dimensional non-Markovian backward stochastic differential equations (BSDEs) with interactively quadratic generators. Some g…

math.PR2019

Existence and uniqueness of solution to scalar BSDEs with $L exp (I^¼ 2 lo g (1 + L))$ -integrable terminal values: the critical case

Shengjun Fan, Ying Hu

In \cite{HuTang2018ECP}, the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) when the terminal value is $L\exp\le…

math.PR2013

Multidimensional BSDEs with uniformly continuous generators and general time intervals

Shengjun Fan, Lishun Xiao, Yanbin Wang

This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y, z)$ n…

math.PR2024

On the existence and uniqueness of unbounded solutions to quadratic BSDEs with monotonic-convex generators

Yan Wang, Xinying Li, Chuang Gu +1

With the terminal value $I^¾^{-}$ admitting a certain exponential moment and $I^¾^{+}$ admitting every exponential moments or being bounded, we establish several existence and uniqueness…

math.PR2022

Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations

Shengjun Fan, Tianxiao Wang, Jiongmin Yong

In this paper, a systematic investigation is carried out for the general solvability of multi-dimensional backward stochastic Volterra integral equations (BSVIEs) with the generato…

math.PR2026

Weighted $L^{p}$ solutions of scalar BSDEs with general unbounded stochastic coefficients

Yaqi Zhang, Zongjia Zhu, Shengjun Fan

This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs in short) with a general random terminal time $I ¨ $ taking values in the extended…

math.PR2023

Scalar BSDEs of iterated-logarithmically sublinear generators with integrable terminal values

Shengjun Fan, Ying Hu, Shanjian Tang

We establish a general existence and uniqueness of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator…

math.PR2025

Existence and uniqueness on $L^{1}$ solutions of multidimensional BSDEs with generators of stochastic one-sided Osgood type

Yuru Lai, Xinying Li, Shengjun Fan

By imposing an additional integrability condition on the first component of the solution, this paper establishes an existence and uniqueness result for $L^{1}$ solutions of multidime…

math.PR2020

Multi-dimensional backward stochastic differential equations of diagonally quadratic generators: the general result

Shengjun Fan, Ying Hu, Shanjian Tang

This paper is devoted to a general solvability of a multi-dimensional backward stochastic differential equation (BSDE) of a diagonally quadratic generator $g (t, y, z)$ , by relaxing t…

math.PR2019

Existence, uniqueness, comparison theorem and stability theorem for unbounded solutions of scalar BSDEs with sub-quadratic generators

Shengjun Fan, Ying Hu

We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $…

math.PR2016

$L^{p} (p > 1)$ solutions of BSDEs with generators satisfying some non-uniform conditions in $t$ and $I ¨ $

Yajun Liu, Depeng Li, Shengjun Fan

This paper is devoted to the $L^{p}$ ( $p > 1$ ) solutions of one-dimensional backward stochastic differential equations (BSDEs for short) with general time intervals and generators sati…

math.PR2019

On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions

Shengjun Fan, Ying Hu, Shanjian Tang

We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator $g$ may b…

math.PR2017

Probabilistic interpretation of HJB equations by the representation theorem for generators of BSDEs

Lishun Xiao, Shengjun Fan, Dejian Tian

The purpose of this note is to propose a new approach for the probabilistic interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic recursive optimal control…

Publications (27)

Invariant representation for generators of general time interval quadratic BSDEs under stochastic growth conditions

On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions: the certain exponential moment case

Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs

Weighted Lp (p≥1) solutions of random time horizon BSDEs with stochastic monotonicity generators

Solvability of BSDEs with possibly unbounded stochastic coefficients on a general weighted Lp space

A representation theorem for generators of BSDEs with general growth generators in y and its applications

1D nonlinear backward stochastic differential equations: a unified theory and applications

Uniqueness of adapted solutions to scalar BSDEs with Peano-type generators

Unbounded Dynamic Concave Utilities via BSDEs

General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition

Weighted solutions of random time horizon BSDEs with stochastic monotonicity and general growth generators and related PDEs

Lp solutions of doubly reflected BSDEs under general assumptions

Existence, uniqueness and comparison theorem on unbounded solutions of general time interval BSDEs with sub-quadratic generators

Lp (p≥1) solutions of multidimensional BSDEs with monotone generators in general time intervals

Multi-dimensional non-Markovian backward stochastic differential equations of interactively quadratic generators

Existence and uniqueness of solution to scalar BSDEs with Lexp(I^¼2log(1+L)​)-integrable terminal values: the critical case

Multidimensional BSDEs with uniformly continuous generators and general time intervals

On the existence and uniqueness of unbounded solutions to quadratic BSDEs with monotonic-convex generators

Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations

Weighted Lp solutions of scalar BSDEs with general unbounded stochastic coefficients

Scalar BSDEs of iterated-logarithmically sublinear generators with integrable terminal values

Existence and uniqueness on L1 solutions of multidimensional BSDEs with generators of stochastic one-sided Osgood type

Multi-dimensional backward stochastic differential equations of diagonally quadratic generators: the general result

Existence, uniqueness, comparison theorem and stability theorem for unbounded solutions of scalar BSDEs with sub-quadratic generators

Lp (p>1) solutions of BSDEs with generators satisfying some non-uniform conditions in t and I¨

On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions

Probabilistic interpretation of HJB equations by the representation theorem for generators of BSDEs

Weighted $L^{p} (p \geq 1)$ solutions of random time horizon BSDEs with stochastic monotonicity generators

Solvability of BSDEs with possibly unbounded stochastic coefficients on a general weighted $L^{p}$ space

A representation theorem for generators of BSDEs with general growth generators in $y$ and its applications

$L^{p}$ solutions of doubly reflected BSDEs under general assumptions

$L^{p}$ $(p \geq 1)$ solutions of multidimensional BSDEs with monotone generators in general time intervals

Existence and uniqueness of solution to scalar BSDEs with $L exp (I^¼ 2 lo g (1 + L))$ -integrable terminal values: the critical case

Weighted $L^{p}$ solutions of scalar BSDEs with general unbounded stochastic coefficients

Existence and uniqueness on $L^{1}$ solutions of multidimensional BSDEs with generators of stochastic one-sided Osgood type

$L^{p} (p > 1)$ solutions of BSDEs with generators satisfying some non-uniform conditions in $t$ and $I ¨ $