Radner equilibrium and systems of quadratic BSDEs with discontinuous generators

关于倒向随机微分方程（BSDEs）的若干思考

Reflections on BSDEs

该研究针对生成元关于纯不连续过程积分的加权$\u2112^2$数据场景，证明了BSDE及带可选障碍的反射BSDE的适定性，实现了离散与连续时间情形的统一处理，验证了结果的最优性并给出比较原理的充分条件。

$L^1$ solutions to one-dimensional BSDEs with sublinear growth generators in $z$

This paper aims at solving a one-dimensional backward stochastic differential equation (BSDE for short) with only integrable parameters. We first establish the existence of a minimal $L^1$ solution for the BSDE when the generator $g$ is stronger continuous in $(y,z)$ and monotonic in $y$ as well as it has a general growth in $y$ and a sublinear growth in $z$. Particularly, the $g$ may be not uniformly continuous in $z$. Then, we put forward and prove a comparison theorem and a Levi type theorem on the minimal $L^1$ solutions. A Lebesgue type theorem on $L^1$ solutions is also obtained. Further…

Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values

We solve a class of BSDE with a power function $f(y) = y^q$, $q > 1$, driving its drift and with the terminal boundary condition $ ξ= \infty \cdot \mathbf{1}_{B(m,r)^c}$ (for which $q > 2$ is assumed) or $ ξ= \infty \cdot \mathbf{1}_{B(m,r)}$, where $B(m,r)$ is the ball in the path space $C([0,T])$ of the underlying Brownian motion centered at the constant function $m$ and radius $r$. The solution involves the derivation and solution of a related heat equation in which $f$ serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although t…

一般McKean-Vlasov和平均场BSDE的存在性、唯一性与混沌传播

Existence, uniqueness and propagation of chaos for general McKean-Vlasov and mean-field BSDEs

本文研究一般设置下平均场和McKean-Vlasov BSDE的存在唯一性，并提出新耦合技术证明混沌传播及其收敛速率，无需解的可交换性。

Existence, uniqueness and strict comparison theorems for backward stochastic differential equations driven by RCLL martingales

Results on the existence, uniqueness and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are established. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models with jumps, including as particular cases the setups studied by Peng and Xu \cite{PX2009,PX2010} and Dumitrescu et al. \cite{DGQS2018} who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.

带跳和随机单调生成元的BSDE的$\mathbb{L}^p$ $(p>1)$-解

$\mathbb{L}^p$ $(p>1)$-solutions for BSDEs with jumps and stochastic monotone generator

研究带跳和多维不连续倒向随机微分方程，在生成元满足随机单调性和随机Lipschitz条件下，建立了$p\geq2$和$p\in(1,2)$时$\mathbb{L}^p$解的存在唯一性。

Homogenization of semi-linear PDEs with discontinuous effective coefficients

We study the asymptotic behavior of solution of semi-linear PDEs. Neither periodicity nor ergodicity will be assumed. In return, we assume that the coefficients admit a limit in Cesaro sense. In such a case, the averaged coefficients could be discontinuous. We use probabilistic approach based on weak convergence for the associated backward stochastic differential equation in the S-topology to derive the averaged PDE. However, since the averaged coefficients are discontinuous, the classical viscosity solution is not defined for the averaged PDE. We then use the notion of "$L^p-$viscosity soluti…

一般滤子空间上由右连左极增过程驱动的带不规则障碍的广义反射倒向随机微分方程

Generalized reflected BSDEs with irregular obstacles driven by RCLL increasing processes on general filtered space

该研究在一般滤子空间上，针对由RCLL增过程驱动的GBSDEs和GRBSDEs，建立了存在唯一性等结果，提出两种方法求解特定GRBSDEs并推广到一般利普希茨情形。

具有非Lipschitz漂移的耦合前向-后向SDE的密度分析及其应用

Density Analysis for coupled forward-backward SDEs with non-Lipschitz drifts and Applications

本文研究了具有非Lipschitz漂移的耦合二次前向-后向SDEs解的密度存在性，提出基于弱解耦场和Itô-Tanaka技巧的框架，并应用于利率模型与不可交易资产的对冲问题。