83 citations · 230 across the 51 of their papers we have counts for
35 papers · 1 filter
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…
Multi-dimensional Mean-field Type Backward Stochastic Differential Equations with Diagonally Quadratic Generators
Shanjian Tang, Guang Yang
In this paper, we study the multi-dimensional backward stochastic differential equations (BSDEs) whose generator depends also on the mean of both variables. When the generator is d…
Multidimensional Backward Stochastic Differential Equations with Rough Drifts
Jiahao Liang, Shanjian Tang
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of th…
Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth
Tao Hao, Ying Hu, Shanjian Tang +1
In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and glo…
The obstacle problem for stochastic porous media equations
Ruoyang Liu, Shanjian Tang
We prove the existence and uniqueness of non-negative entropy solutions of the obstacle problem for stochastic porous media equations. The core of the method is to combine the entr…
State-Density Flows of Non-Degenerate Density-Dependent Mean Field SDEs and Associated PDEs
Ziyu Huang, Shanjian Tang
In this paper, we study a combined system of a Fokker-Planck (FP) equation for with initial , and a stochastic differential equatio…
Classical solution of path-dependent mean-field semilinear PDEs
Shanjian Tang, Huilin Zhang
The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which…
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…
Fully Coupled Nonlocal Quasilinear Forward-Backward Parabolic Equations Arising from Mean Field Games
Ziyu Huang, Shanjian Tang
In this paper, we study fully coupled nonlocal second order quasilinear forward-backward partial differential equations (FBPDEs), which arise from solution of the mean field game (…
Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection
Dingqian Sun, Gechun Liang, Shanjian Tang
We study the quantitative stability of the solutions to Markovian quadratic reflected BSDEs with bounded terminal data. By virtue of BMO martingale and change of measure techniques…
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 , by relaxing t…
Reflected Quadratic BSDEs driven by -Brownian Motions
Dong Cao, Shanjian Tang
In this paper, we consider a reflected backward stochastic differential equation driven by a -Brownian motion (-BSDE), with the generator growing quadratically in the second…
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 may b…
Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: a probabilistic approach
Jun Dai, Shanjian Tang, Bingjie Wu
In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of…
Systems of ergodic BSDEs arising in regime switching forward performance processes
Ying Hu, Gechun Liang, Shanjian Tang
We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such syste…
Uniqueness of solution to scalar BSDEs with -integrable terminal values
Rainer Buckdahn, Ying Hu, Shanjian Tang
In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $L\exp{\left(μ\sqrt{2\log{(1…
Mean-field type Quadratic BSDEs
Hélène Hibon, Ying Hu, Shanjian Tang
In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-…
Utility maximization in constrained and unbounded financial markets: Applications to indifference valuation, regime switching, consumption and Epstein-Zin recursive utility
Ying Hu, Gechun Liang, Shanjian Tang
This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (200…
Existence of solution to scalar BSDEs with weakly -integrable terminal values
Ying Hu, Shanjian Tang
In this paper, we study a scalar linearly growing BSDE with a weakly -integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies som…
Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators
Ying Hu, Shanjian Tang
The paper is concerned with adapted solution of a multi-dimensional BSDE with a "diagonally" quadratic generator, the quadratic part of whose th component only depends on the $i…
Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain
Juan Li, Shanjian Tang
In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined vi…
-Solution () of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space
Kai Du, Shanjian Tang, Qi Zhang
In this paper, we consider the backward Cauchy problem of linear degenerate stochastic partial differential equations. We obtain the existence and uniqueness results in Sobolev spa…
2D Backward Stochastic Navier-Stokes Equations with Nonlinear Forcing
Jinniao Qiu, Shanjian Tang, Yuncheng You
The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Br…
Maximum Principle for Quasi-linear Backward Stochastic Partial Differential Equations
Jinniao Qiu, Shanjian Tang
In this paper we are concerned with the maximum principle for quasi-linear backward stochastic partial differential equations (BSPDEs for short) of parabolic type. We first prove t…